diff options
author | Joel Sherrill <joel.sherrill@OARcorp.com> | 2011-04-08 17:33:11 +0000 |
---|---|---|
committer | Joel Sherrill <joel.sherrill@OARcorp.com> | 2011-04-08 17:33:11 +0000 |
commit | 73f643f3f4a55310b2c8c1a9858906b2dd676e72 (patch) | |
tree | b1df97f18dace4a5702b0bc7aafdfee8a2f25ada /gsl-1.9/doc/statistics.texi | |
parent | ee523abdace8337d05ec4a179fcdf5de3fe0f634 (diff) |
2011-04-08 Joel Sherrill <joel.sherrill@oarcorp.com>
* AUTHORS, BUGS, COPYING, ChangeLog, INSTALL, Makefile.am, Makefile.in,
NEWS, README, SUPPORT, THANKS, TODO, acconfig.h, aclocal.m4,
autogen.sh, config.guess, config.h.in, config.sub, configure,
configure.ac, gsl-config.in, gsl-histogram.c, gsl-randist.c, gsl.m4,
gsl.pc.in, gsl.spec.in, gsl_machine.h, gsl_math.h, gsl_mode.h,
gsl_nan.h, gsl_pow_int.h, gsl_precision.h, gsl_types.h,
gsl_version.h.in, install-sh, ltmain.sh, mdate-sh, missing,
mkinstalldirs, templates_off.h, templates_on.h,
test_gsl_histogram.sh, version.c, blas/ChangeLog, blas/Makefile.am,
blas/Makefile.in, blas/TODO, blas/blas.c, blas/gsl_blas.h,
blas/gsl_blas_types.h, block/ChangeLog, block/Makefile.am,
block/Makefile.in, block/block.c, block/block_source.c, block/file.c,
block/fprintf_source.c, block/fwrite_source.c, block/gsl_block.h,
block/gsl_block_char.h, block/gsl_block_complex_double.h,
block/gsl_block_complex_float.h,
block/gsl_block_complex_long_double.h, block/gsl_block_double.h,
block/gsl_block_float.h, block/gsl_block_int.h,
block/gsl_block_long.h, block/gsl_block_long_double.h,
block/gsl_block_short.h, block/gsl_block_uchar.h,
block/gsl_block_uint.h, block/gsl_block_ulong.h,
block/gsl_block_ushort.h, block/gsl_check_range.h, block/init.c,
block/init_source.c, block/test.c, block/test_complex_io.c,
block/test_complex_source.c, block/test_io.c, block/test_source.c,
bspline/ChangeLog, bspline/Makefile.am, bspline/Makefile.in,
bspline/TODO, bspline/bspline.c, bspline/gsl_bspline.h,
bspline/test.c, cblas/ChangeLog, cblas/Makefile.am,
cblas/Makefile.in, cblas/TODO, cblas/caxpy.c, cblas/cblas.h,
cblas/ccopy.c, cblas/cdotc_sub.c, cblas/cdotu_sub.c, cblas/cgbmv.c,
cblas/cgemm.c, cblas/cgemv.c, cblas/cgerc.c, cblas/cgeru.c,
cblas/chbmv.c, cblas/chemm.c, cblas/chemv.c, cblas/cher.c,
cblas/cher2.c, cblas/cher2k.c, cblas/cherk.c, cblas/chpmv.c,
cblas/chpr.c, cblas/chpr2.c, cblas/cscal.c, cblas/csscal.c,
cblas/cswap.c, cblas/csymm.c, cblas/csyr2k.c, cblas/csyrk.c,
cblas/ctbmv.c, cblas/ctbsv.c, cblas/ctpmv.c, cblas/ctpsv.c,
cblas/ctrmm.c, cblas/ctrmv.c, cblas/ctrsm.c, cblas/ctrsv.c,
cblas/dasum.c, cblas/daxpy.c, cblas/dcopy.c, cblas/ddot.c,
cblas/dgbmv.c, cblas/dgemm.c, cblas/dgemv.c, cblas/dger.c,
cblas/dnrm2.c, cblas/drot.c, cblas/drotg.c, cblas/drotm.c,
cblas/drotmg.c, cblas/dsbmv.c, cblas/dscal.c, cblas/dsdot.c,
cblas/dspmv.c, cblas/dspr.c, cblas/dspr2.c, cblas/dswap.c,
cblas/dsymm.c, cblas/dsymv.c, cblas/dsyr.c, cblas/dsyr2.c,
cblas/dsyr2k.c, cblas/dsyrk.c, cblas/dtbmv.c, cblas/dtbsv.c,
cblas/dtpmv.c, cblas/dtpsv.c, cblas/dtrmm.c, cblas/dtrmv.c,
cblas/dtrsm.c, cblas/dtrsv.c, cblas/dzasum.c, cblas/dznrm2.c,
cblas/gsl_cblas.h, cblas/hypot.c, cblas/icamax.c, cblas/idamax.c,
cblas/isamax.c, cblas/izamax.c, cblas/sasum.c, cblas/saxpy.c,
cblas/scasum.c, cblas/scnrm2.c, cblas/scopy.c, cblas/sdot.c,
cblas/sdsdot.c, cblas/sgbmv.c, cblas/sgemm.c, cblas/sgemv.c,
cblas/sger.c, cblas/snrm2.c, cblas/source_asum_c.h,
cblas/source_asum_r.h, cblas/source_axpy_c.h, cblas/source_axpy_r.h,
cblas/source_copy_c.h, cblas/source_copy_r.h, cblas/source_dot_c.h,
cblas/source_dot_r.h, cblas/source_gbmv_c.h, cblas/source_gbmv_r.h,
cblas/source_gemm_c.h, cblas/source_gemm_r.h, cblas/source_gemv_c.h,
cblas/source_gemv_r.h, cblas/source_ger.h, cblas/source_gerc.h,
cblas/source_geru.h, cblas/source_hbmv.h, cblas/source_hemm.h,
cblas/source_hemv.h, cblas/source_her.h, cblas/source_her2.h,
cblas/source_her2k.h, cblas/source_herk.h, cblas/source_hpmv.h,
cblas/source_hpr.h, cblas/source_hpr2.h, cblas/source_iamax_c.h,
cblas/source_iamax_r.h, cblas/source_nrm2_c.h, cblas/source_nrm2_r.h,
cblas/source_rot.h, cblas/source_rotg.h, cblas/source_rotm.h,
cblas/source_rotmg.h, cblas/source_sbmv.h, cblas/source_scal_c.h,
cblas/source_scal_c_s.h, cblas/source_scal_r.h, cblas/source_spmv.h,
cblas/source_spr.h, cblas/source_spr2.h, cblas/source_swap_c.h,
cblas/source_swap_r.h, cblas/source_symm_c.h, cblas/source_symm_r.h,
cblas/source_symv.h, cblas/source_syr.h, cblas/source_syr2.h,
cblas/source_syr2k_c.h, cblas/source_syr2k_r.h,
cblas/source_syrk_c.h, cblas/source_syrk_r.h, cblas/source_tbmv_c.h,
cblas/source_tbmv_r.h, cblas/source_tbsv_c.h, cblas/source_tbsv_r.h,
cblas/source_tpmv_c.h, cblas/source_tpmv_r.h, cblas/source_tpsv_c.h,
cblas/source_tpsv_r.h, cblas/source_trmm_c.h, cblas/source_trmm_r.h,
cblas/source_trmv_c.h, cblas/source_trmv_r.h, cblas/source_trsm_c.h,
cblas/source_trsm_r.h, cblas/source_trsv_c.h, cblas/source_trsv_r.h,
cblas/srot.c, cblas/srotg.c, cblas/srotm.c, cblas/srotmg.c,
cblas/ssbmv.c, cblas/sscal.c, cblas/sspmv.c, cblas/sspr.c,
cblas/sspr2.c, cblas/sswap.c, cblas/ssymm.c, cblas/ssymv.c,
cblas/ssyr.c, cblas/ssyr2.c, cblas/ssyr2k.c, cblas/ssyrk.c,
cblas/stbmv.c, cblas/stbsv.c, cblas/stpmv.c, cblas/stpsv.c,
cblas/strmm.c, cblas/strmv.c, cblas/strsm.c, cblas/strsv.c,
cblas/test.c, cblas/test_amax.c, cblas/test_asum.c,
cblas/test_axpy.c, cblas/test_copy.c, cblas/test_dot.c,
cblas/test_gbmv.c, cblas/test_gemm.c, cblas/test_gemv.c,
cblas/test_ger.c, cblas/test_hbmv.c, cblas/test_hemm.c,
cblas/test_hemv.c, cblas/test_her.c, cblas/test_her2.c,
cblas/test_her2k.c, cblas/test_herk.c, cblas/test_hpmv.c,
cblas/test_hpr.c, cblas/test_hpr2.c, cblas/test_nrm2.c,
cblas/test_rot.c, cblas/test_rotg.c, cblas/test_rotm.c,
cblas/test_rotmg.c, cblas/test_sbmv.c, cblas/test_scal.c,
cblas/test_spmv.c, cblas/test_spr.c, cblas/test_spr2.c,
cblas/test_swap.c, cblas/test_symm.c, cblas/test_symv.c,
cblas/test_syr.c, cblas/test_syr2.c, cblas/test_syr2k.c,
cblas/test_syrk.c, cblas/test_tbmv.c, cblas/test_tbsv.c,
cblas/test_tpmv.c, cblas/test_tpsv.c, cblas/test_trmm.c,
cblas/test_trmv.c, cblas/test_trsm.c, cblas/test_trsv.c,
cblas/tests.c, cblas/tests.h, cblas/xerbla.c, cblas/zaxpy.c,
cblas/zcopy.c, cblas/zdotc_sub.c, cblas/zdotu_sub.c, cblas/zdscal.c,
cblas/zgbmv.c, cblas/zgemm.c, cblas/zgemv.c, cblas/zgerc.c,
cblas/zgeru.c, cblas/zhbmv.c, cblas/zhemm.c, cblas/zhemv.c,
cblas/zher.c, cblas/zher2.c, cblas/zher2k.c, cblas/zherk.c,
cblas/zhpmv.c, cblas/zhpr.c, cblas/zhpr2.c, cblas/zscal.c,
cblas/zswap.c, cblas/zsymm.c, cblas/zsyr2k.c, cblas/zsyrk.c,
cblas/ztbmv.c, cblas/ztbsv.c, cblas/ztpmv.c, cblas/ztpsv.c,
cblas/ztrmm.c, cblas/ztrmv.c, cblas/ztrsm.c, cblas/ztrsv.c,
cdf/ChangeLog, cdf/Makefile.am, cdf/Makefile.in, cdf/beta.c,
cdf/beta_inc.c, cdf/betainv.c, cdf/binomial.c, cdf/cauchy.c,
cdf/cauchyinv.c, cdf/chisq.c, cdf/chisqinv.c, cdf/error.h,
cdf/exponential.c, cdf/exponentialinv.c, cdf/exppow.c, cdf/fdist.c,
cdf/fdistinv.c, cdf/flat.c, cdf/flatinv.c, cdf/gamma.c,
cdf/gammainv.c, cdf/gauss.c, cdf/gaussinv.c, cdf/geometric.c,
cdf/gsl_cdf.h, cdf/gumbel1.c, cdf/gumbel1inv.c, cdf/gumbel2.c,
cdf/gumbel2inv.c, cdf/hypergeometric.c, cdf/laplace.c,
cdf/laplaceinv.c, cdf/logistic.c, cdf/logisticinv.c, cdf/lognormal.c,
cdf/lognormalinv.c, cdf/nbinomial.c, cdf/pareto.c, cdf/paretoinv.c,
cdf/pascal.c, cdf/poisson.c, cdf/rat_eval.h, cdf/rayleigh.c,
cdf/rayleighinv.c, cdf/tdist.c, cdf/tdistinv.c, cdf/test.c,
cdf/test_auto.c, cdf/weibull.c, cdf/weibullinv.c, cheb/ChangeLog,
cheb/Makefile.am, cheb/Makefile.in, cheb/deriv.c, cheb/eval.c,
cheb/gsl_chebyshev.h, cheb/init.c, cheb/integ.c, cheb/test.c,
combination/ChangeLog, combination/Makefile.am,
combination/Makefile.in, combination/combination.c,
combination/file.c, combination/gsl_combination.h,
combination/init.c, combination/test.c, complex/ChangeLog,
complex/Makefile.am, complex/Makefile.in, complex/TODO,
complex/gsl_complex.h, complex/gsl_complex_math.h, complex/math.c,
complex/results.h, complex/results1.h, complex/results_real.h,
complex/test.c, const/ChangeLog, const/Makefile.am,
const/Makefile.in, const/TODO, const/gsl_const.h,
const/gsl_const_cgs.h, const/gsl_const_cgsm.h, const/gsl_const_mks.h,
const/gsl_const_mksa.h, const/gsl_const_num.h, const/test.c,
deriv/ChangeLog, deriv/Makefile.am, deriv/Makefile.in, deriv/deriv.c,
deriv/gsl_deriv.h, deriv/test.c, dht/ChangeLog, dht/Makefile.am,
dht/Makefile.in, dht/dht.c, dht/gsl_dht.h, dht/test.c,
diff/ChangeLog, diff/Makefile.am, diff/Makefile.in, diff/diff.c,
diff/gsl_diff.h, diff/test.c, doc/12-cities.eps, doc/ChangeLog,
doc/Makefile.am, doc/Makefile.in, doc/algorithm.sty,
doc/algorithmic.sty, doc/autoconf.texi, doc/blas.texi,
doc/bspline.eps, doc/bspline.texi, doc/calc.sty, doc/cblas.texi,
doc/cheb.eps, doc/cheb.texi, doc/combination.texi, doc/complex.texi,
doc/const.texi, doc/debug.texi, doc/dht.texi, doc/diff.texi,
doc/dwt-orig.eps, doc/dwt-samp.eps, doc/dwt.texi, doc/eigen.texi,
doc/err.texi, doc/fdl.texi, doc/fft-complex-radix2-f.eps,
doc/fft-complex-radix2-t.eps, doc/fft-complex-radix2.eps,
doc/fft-real-mixedradix.eps, doc/fft.texi, doc/fftalgorithms.bib,
doc/fftalgorithms.tex, doc/final-route.eps, doc/fit-exp.eps,
doc/fit-wlinear.eps, doc/fit-wlinear2.eps, doc/fitting.texi,
doc/freemanuals.texi, doc/gpl.texi, doc/gsl-config.1,
doc/gsl-design.texi, doc/gsl-histogram.1, doc/gsl-randist.1,
doc/gsl-ref.info, doc/gsl-ref.info-1, doc/gsl-ref.info-2,
doc/gsl-ref.info-3, doc/gsl-ref.info-4, doc/gsl-ref.info-5,
doc/gsl-ref.info-6, doc/gsl-ref.texi, doc/gsl.3, doc/histogram.eps,
doc/histogram.texi, doc/histogram2d.eps, doc/ieee754.texi,
doc/initial-route.eps, doc/integration.texi, doc/interp.texi,
doc/interp2.eps, doc/interpp2.eps, doc/intro.texi, doc/landau.dat,
doc/linalg.texi, doc/math.texi, doc/mdate-sh, doc/min-interval.eps,
doc/min.texi, doc/montecarlo.texi, doc/multifit.texi,
doc/multimin.eps, doc/multimin.texi, doc/multiroots.texi,
doc/ntuple.eps, doc/ntuple.texi, doc/ode-initval.texi,
doc/permutation.texi, doc/poly.texi, doc/qrng.eps, doc/qrng.texi,
doc/rand-bernoulli.tex, doc/rand-beta.tex, doc/rand-binomial.tex,
doc/rand-bivariate-gaussian.tex, doc/rand-cauchy.tex,
doc/rand-chisq.tex, doc/rand-erlang.tex, doc/rand-exponential.tex,
doc/rand-exppow.tex, doc/rand-fdist.tex, doc/rand-flat.tex,
doc/rand-gamma.tex, doc/rand-gaussian-tail.tex,
doc/rand-gaussian.tex, doc/rand-geometric.tex, doc/rand-gumbel.tex,
doc/rand-gumbel1.tex, doc/rand-gumbel2.tex,
doc/rand-hypergeometric.tex, doc/rand-landau.tex,
doc/rand-laplace.tex, doc/rand-levy.tex, doc/rand-levyskew.tex,
doc/rand-logarithmic.tex, doc/rand-logistic.tex,
doc/rand-lognormal.tex, doc/rand-nbinomial.tex, doc/rand-pareto.tex,
doc/rand-pascal.tex, doc/rand-poisson.tex,
doc/rand-rayleigh-tail.tex, doc/rand-rayleigh.tex,
doc/rand-tdist.tex, doc/rand-weibull.tex, doc/randist.texi,
doc/random-walk.tex, doc/randplots.gnp, doc/rng.texi,
doc/roots-bisection.eps, doc/roots-false-position.eps,
doc/roots-newtons-method.eps, doc/roots-secant-method.eps,
doc/roots.texi, doc/siman-energy.eps, doc/siman-test.eps,
doc/siman.texi, doc/sort.texi, doc/specfunc-airy.texi,
doc/specfunc-bessel.texi, doc/specfunc-clausen.texi,
doc/specfunc-coulomb.texi, doc/specfunc-coupling.texi,
doc/specfunc-dawson.texi, doc/specfunc-debye.texi,
doc/specfunc-dilog.texi, doc/specfunc-elementary.texi,
doc/specfunc-ellint.texi, doc/specfunc-elljac.texi,
doc/specfunc-erf.texi, doc/specfunc-exp.texi,
doc/specfunc-expint.texi, doc/specfunc-fermi-dirac.texi,
doc/specfunc-gamma.texi, doc/specfunc-gegenbauer.texi,
doc/specfunc-hyperg.texi, doc/specfunc-laguerre.texi,
doc/specfunc-lambert.texi, doc/specfunc-legendre.texi,
doc/specfunc-log.texi, doc/specfunc-mathieu.texi,
doc/specfunc-pow-int.texi, doc/specfunc-psi.texi,
doc/specfunc-synchrotron.texi, doc/specfunc-transport.texi,
doc/specfunc-trig.texi, doc/specfunc-zeta.texi, doc/specfunc.texi,
doc/stamp-vti, doc/statistics.texi, doc/sum.texi, doc/texinfo.tex,
doc/usage.texi, doc/vdp.eps, doc/vectors.texi, doc/version-ref.texi,
doc/examples/blas.c, doc/examples/blas.out, doc/examples/block.c,
doc/examples/block.out, doc/examples/bspline.c, doc/examples/cblas.c,
doc/examples/cblas.out, doc/examples/cdf.c, doc/examples/cdf.out,
doc/examples/cheb.c, doc/examples/combination.c,
doc/examples/combination.out, doc/examples/const.c,
doc/examples/const.out, doc/examples/demo_fn.c,
doc/examples/demo_fn.h, doc/examples/diff.c, doc/examples/diff.out,
doc/examples/dwt.c, doc/examples/dwt.dat, doc/examples/ecg.dat,
doc/examples/eigen.c, doc/examples/eigen_nonsymm.c,
doc/examples/expfit.c, doc/examples/fft.c, doc/examples/fftmr.c,
doc/examples/fftreal.c, doc/examples/fitting.c,
doc/examples/fitting2.c, doc/examples/fitting3.c,
doc/examples/histogram.c, doc/examples/histogram2d.c,
doc/examples/ieee.c, doc/examples/ieeeround.c,
doc/examples/integration.c, doc/examples/integration.out,
doc/examples/interp.c, doc/examples/interpp.c, doc/examples/intro.c,
doc/examples/intro.out, doc/examples/linalglu.c,
doc/examples/linalglu.out, doc/examples/matrix.c,
doc/examples/matrixw.c, doc/examples/min.c, doc/examples/min.out,
doc/examples/monte.c, doc/examples/nlfit.c, doc/examples/ntupler.c,
doc/examples/ntuplew.c, doc/examples/ode-initval.c,
doc/examples/odefixed.c, doc/examples/permseq.c,
doc/examples/permshuffle.c, doc/examples/polyroots.c,
doc/examples/polyroots.out, doc/examples/qrng.c,
doc/examples/randpoisson.2.out, doc/examples/randpoisson.c,
doc/examples/randpoisson.out, doc/examples/randwalk.c,
doc/examples/rng.c, doc/examples/rng.out, doc/examples/rngunif.2.out,
doc/examples/rngunif.c, doc/examples/rngunif.out,
doc/examples/rootnewt.c, doc/examples/roots.c, doc/examples/siman.c,
doc/examples/sortsmall.c, doc/examples/sortsmall.out,
doc/examples/specfun.c, doc/examples/specfun.out,
doc/examples/specfun_e.c, doc/examples/specfun_e.out,
doc/examples/stat.c, doc/examples/stat.out, doc/examples/statsort.c,
doc/examples/statsort.out, doc/examples/sum.c, doc/examples/sum.out,
doc/examples/vector.c, doc/examples/vectorr.c,
doc/examples/vectorview.c, doc/examples/vectorview.out,
doc/examples/vectorw.c, eigen/ChangeLog, eigen/Makefile.am,
eigen/Makefile.in, eigen/TODO, eigen/francis.c, eigen/gsl_eigen.h,
eigen/herm.c, eigen/hermv.c, eigen/jacobi.c, eigen/nonsymm.c,
eigen/nonsymmv.c, eigen/qrstep.c, eigen/schur.c, eigen/schur.h,
eigen/sort.c, eigen/symm.c, eigen/symmv.c, eigen/test.c,
err/ChangeLog, err/Makefile.am, err/Makefile.in, err/TODO,
err/error.c, err/gsl_errno.h, err/gsl_message.h, err/message.c,
err/stream.c, err/strerror.c, err/test.c, fft/ChangeLog,
fft/Makefile.am, fft/Makefile.in, fft/TODO, fft/bitreverse.c,
fft/bitreverse.h, fft/c_init.c, fft/c_main.c, fft/c_pass.h,
fft/c_pass_2.c, fft/c_pass_3.c, fft/c_pass_4.c, fft/c_pass_5.c,
fft/c_pass_6.c, fft/c_pass_7.c, fft/c_pass_n.c, fft/c_radix2.c,
fft/compare.h, fft/compare_source.c, fft/complex_internal.h,
fft/dft.c, fft/dft_source.c, fft/factorize.c, fft/factorize.h,
fft/fft.c, fft/gsl_dft_complex.h, fft/gsl_dft_complex_float.h,
fft/gsl_fft.h, fft/gsl_fft_complex.h, fft/gsl_fft_complex_float.h,
fft/gsl_fft_halfcomplex.h, fft/gsl_fft_halfcomplex_float.h,
fft/gsl_fft_real.h, fft/gsl_fft_real_float.h, fft/hc_init.c,
fft/hc_main.c, fft/hc_pass.h, fft/hc_pass_2.c, fft/hc_pass_3.c,
fft/hc_pass_4.c, fft/hc_pass_5.c, fft/hc_pass_n.c, fft/hc_radix2.c,
fft/hc_unpack.c, fft/real_init.c, fft/real_main.c, fft/real_pass.h,
fft/real_pass_2.c, fft/real_pass_3.c, fft/real_pass_4.c,
fft/real_pass_5.c, fft/real_pass_n.c, fft/real_radix2.c,
fft/real_unpack.c, fft/signals.c, fft/signals.h,
fft/signals_source.c, fft/test.c, fft/test_complex_source.c,
fft/test_real_source.c, fft/test_trap_source.c, fft/urand.c,
fit/ChangeLog, fit/Makefile.am, fit/Makefile.in, fit/gsl_fit.h,
fit/linear.c, fit/test.c, gsl/Makefile.am, gsl/Makefile.in,
histogram/ChangeLog, histogram/Makefile.am, histogram/Makefile.in,
histogram/TODO, histogram/add.c, histogram/add2d.c,
histogram/calloc_range.c, histogram/calloc_range2d.c,
histogram/copy.c, histogram/copy2d.c, histogram/file.c,
histogram/file2d.c, histogram/find.c, histogram/find2d.c,
histogram/get.c, histogram/get2d.c, histogram/gsl_histogram.h,
histogram/gsl_histogram2d.h, histogram/init.c, histogram/init2d.c,
histogram/maxval.c, histogram/maxval2d.c, histogram/oper.c,
histogram/oper2d.c, histogram/params.c, histogram/params2d.c,
histogram/pdf.c, histogram/pdf2d.c, histogram/reset.c,
histogram/reset2d.c, histogram/stat.c, histogram/stat2d.c,
histogram/test.c, histogram/test1d.c, histogram/test1d_resample.c,
histogram/test1d_trap.c, histogram/test2d.c,
histogram/test2d_resample.c, histogram/test2d_trap.c,
histogram/urand.c, ieee-utils/ChangeLog, ieee-utils/Makefile.am,
ieee-utils/Makefile.in, ieee-utils/TODO, ieee-utils/endian.c,
ieee-utils/env.c, ieee-utils/fp-aix.c, ieee-utils/fp-darwin.c,
ieee-utils/fp-darwin86.c, ieee-utils/fp-freebsd.c,
ieee-utils/fp-gnuc99.c, ieee-utils/fp-gnum68k.c,
ieee-utils/fp-gnuppc.c, ieee-utils/fp-gnusparc.c,
ieee-utils/fp-gnux86.c, ieee-utils/fp-hpux.c, ieee-utils/fp-hpux11.c,
ieee-utils/fp-irix.c, ieee-utils/fp-netbsd.c,
ieee-utils/fp-openbsd.c, ieee-utils/fp-os2emx.c,
ieee-utils/fp-solaris.c, ieee-utils/fp-sunos4.c,
ieee-utils/fp-tru64.c, ieee-utils/fp-unknown.c, ieee-utils/fp.c,
ieee-utils/gsl_ieee_utils.h, ieee-utils/make_rep.c,
ieee-utils/print.c, ieee-utils/read.c, ieee-utils/standardize.c,
ieee-utils/test.c, integration/ChangeLog, integration/Makefile.am,
integration/Makefile.in, integration/TODO, integration/append.c,
integration/err.c, integration/gsl_integration.h,
integration/initialise.c, integration/positivity.c,
integration/ptsort.c, integration/qag.c, integration/qagp.c,
integration/qags.c, integration/qawc.c, integration/qawf.c,
integration/qawo.c, integration/qaws.c, integration/qc25c.c,
integration/qc25f.c, integration/qc25s.c, integration/qcheb.c,
integration/qelg.c, integration/qk.c, integration/qk15.c,
integration/qk21.c, integration/qk31.c, integration/qk41.c,
integration/qk51.c, integration/qk61.c, integration/qmomo.c,
integration/qmomof.c, integration/qng.c, integration/qng.h,
integration/qpsrt.c, integration/qpsrt2.c, integration/reset.c,
integration/set_initial.c, integration/test.c, integration/tests.c,
integration/tests.h, integration/util.c, integration/workspace.c,
interpolation/ChangeLog, interpolation/Makefile.am,
interpolation/Makefile.in, interpolation/TODO, interpolation/accel.c,
interpolation/akima.c, interpolation/bsearch.c,
interpolation/bsearch.h, interpolation/cspline.c,
interpolation/gsl_interp.h, interpolation/gsl_spline.h,
interpolation/integ_eval.h, interpolation/interp.c,
interpolation/linear.c, interpolation/poly.c, interpolation/spline.c,
interpolation/test.c, linalg/ChangeLog, linalg/Makefile.am,
linalg/Makefile.in, linalg/TODO, linalg/apply_givens.c,
linalg/balance.c, linalg/balancemat.c, linalg/bidiag.c,
linalg/cholesky.c, linalg/exponential.c, linalg/givens.c,
linalg/gsl_linalg.h, linalg/hermtd.c, linalg/hessenberg.c,
linalg/hh.c, linalg/householder.c, linalg/householdercomplex.c,
linalg/lq.c, linalg/lu.c, linalg/luc.c, linalg/multiply.c,
linalg/ptlq.c, linalg/qr.c, linalg/qrpt.c, linalg/svd.c,
linalg/svdstep.c, linalg/symmtd.c, linalg/test.c, linalg/tridiag.c,
linalg/tridiag.h, matrix/ChangeLog, matrix/Makefile.am,
matrix/Makefile.in, matrix/TODO, matrix/copy.c, matrix/copy_source.c,
matrix/file.c, matrix/file_source.c, matrix/getset.c,
matrix/getset_source.c, matrix/gsl_matrix.h,
matrix/gsl_matrix_char.h, matrix/gsl_matrix_complex_double.h,
matrix/gsl_matrix_complex_float.h,
matrix/gsl_matrix_complex_long_double.h, matrix/gsl_matrix_double.h,
matrix/gsl_matrix_float.h, matrix/gsl_matrix_int.h,
matrix/gsl_matrix_long.h, matrix/gsl_matrix_long_double.h,
matrix/gsl_matrix_short.h, matrix/gsl_matrix_uchar.h,
matrix/gsl_matrix_uint.h, matrix/gsl_matrix_ulong.h,
matrix/gsl_matrix_ushort.h, matrix/init.c, matrix/init_source.c,
matrix/matrix.c, matrix/matrix_source.c, matrix/minmax.c,
matrix/minmax_source.c, matrix/oper.c, matrix/oper_complex_source.c,
matrix/oper_source.c, matrix/prop.c, matrix/prop_source.c,
matrix/rowcol.c, matrix/rowcol_source.c, matrix/submatrix.c,
matrix/submatrix_source.c, matrix/swap.c, matrix/swap_source.c,
matrix/test.c, matrix/test_complex_source.c, matrix/test_source.c,
matrix/test_static.c, matrix/view.c, matrix/view.h,
matrix/view_source.c, min/ChangeLog, min/Makefile.am,
min/Makefile.in, min/bracketing.c, min/brent.c, min/convergence.c,
min/fsolver.c, min/golden.c, min/gsl_min.h, min/min.h, min/test.c,
min/test.h, min/test_funcs.c, monte/ChangeLog, monte/Makefile.am,
monte/Makefile.in, monte/README, monte/TODO, monte/gsl_monte.h,
monte/gsl_monte_miser.h, monte/gsl_monte_plain.h,
monte/gsl_monte_vegas.h, monte/miser.c, monte/plain.c, monte/test.c,
monte/test_main.c, monte/vegas.c, multifit/ChangeLog,
multifit/Makefile.am, multifit/Makefile.in, multifit/TODO,
multifit/convergence.c, multifit/covar.c, multifit/fdfsolver.c,
multifit/fsolver.c, multifit/gradient.c, multifit/gsl_multifit.h,
multifit/gsl_multifit_nlin.h, multifit/lmder.c, multifit/lmiterate.c,
multifit/lmpar.c, multifit/lmset.c, multifit/lmutil.c,
multifit/multilinear.c, multifit/qrsolv.c, multifit/test.c,
multifit/test_brown.c, multifit/test_enso.c,
multifit/test_estimator.c, multifit/test_filip.c, multifit/test_fn.c,
multifit/test_hahn1.c, multifit/test_kirby2.c,
multifit/test_longley.c, multifit/test_nelson.c,
multifit/test_pontius.c, multifit/work.c, multimin/ChangeLog,
multimin/Makefile.am, multimin/Makefile.in, multimin/TODO,
multimin/conjugate_fr.c, multimin/conjugate_pr.c,
multimin/convergence.c, multimin/diff.c,
multimin/directional_minimize.c, multimin/fdfminimizer.c,
multimin/fminimizer.c, multimin/gsl_multimin.h,
multimin/linear_minimize.c, multimin/linear_wrapper.c,
multimin/simplex.c, multimin/steepest_descent.c, multimin/test.c,
multimin/test_funcs.c, multimin/test_funcs.h, multimin/vector_bfgs.c,
multimin/vector_bfgs2.c, multiroots/ChangeLog,
multiroots/Makefile.am, multiroots/Makefile.in, multiroots/broyden.c,
multiroots/convergence.c, multiroots/dnewton.c, multiroots/dogleg.c,
multiroots/enorm.c, multiroots/fdfsolver.c, multiroots/fdjac.c,
multiroots/fsolver.c, multiroots/gnewton.c,
multiroots/gsl_multiroots.h, multiroots/hybrid.c,
multiroots/hybridj.c, multiroots/newton.c, multiroots/test.c,
multiroots/test_funcs.c, multiroots/test_funcs.h, ntuple/ChangeLog,
ntuple/Makefile.am, ntuple/Makefile.in, ntuple/gsl_ntuple.h,
ntuple/ntuple.c, ntuple/test.c, ode-initval/ChangeLog,
ode-initval/Makefile.am, ode-initval/Makefile.in, ode-initval/TODO,
ode-initval/bsimp.c, ode-initval/control.c, ode-initval/cscal.c,
ode-initval/cstd.c, ode-initval/evolve.c, ode-initval/gear1.c,
ode-initval/gear2.c, ode-initval/gsl_odeiv.h,
ode-initval/odeiv_util.h, ode-initval/rk2.c, ode-initval/rk2imp.c,
ode-initval/rk2simp.c, ode-initval/rk4.c, ode-initval/rk4imp.c,
ode-initval/rk8pd.c, ode-initval/rkck.c, ode-initval/rkf45.c,
ode-initval/step.c, ode-initval/test.c, permutation/ChangeLog,
permutation/Makefile.am, permutation/Makefile.in,
permutation/canonical.c, permutation/file.c,
permutation/gsl_permutation.h, permutation/gsl_permute.h,
permutation/gsl_permute_char.h,
permutation/gsl_permute_complex_double.h,
permutation/gsl_permute_complex_float.h,
permutation/gsl_permute_complex_long_double.h,
permutation/gsl_permute_double.h, permutation/gsl_permute_float.h,
permutation/gsl_permute_int.h, permutation/gsl_permute_long.h,
permutation/gsl_permute_long_double.h,
permutation/gsl_permute_short.h, permutation/gsl_permute_uchar.h,
permutation/gsl_permute_uint.h, permutation/gsl_permute_ulong.h,
permutation/gsl_permute_ushort.h, permutation/gsl_permute_vector.h,
permutation/gsl_permute_vector_char.h,
permutation/gsl_permute_vector_complex_double.h,
permutation/gsl_permute_vector_complex_float.h,
permutation/gsl_permute_vector_complex_long_double.h,
permutation/gsl_permute_vector_double.h,
permutation/gsl_permute_vector_float.h,
permutation/gsl_permute_vector_int.h,
permutation/gsl_permute_vector_long.h,
permutation/gsl_permute_vector_long_double.h,
permutation/gsl_permute_vector_short.h,
permutation/gsl_permute_vector_uchar.h,
permutation/gsl_permute_vector_uint.h,
permutation/gsl_permute_vector_ulong.h,
permutation/gsl_permute_vector_ushort.h, permutation/init.c,
permutation/permutation.c, permutation/permute.c,
permutation/permute_source.c, permutation/test.c, poly/ChangeLog,
poly/Makefile.am, poly/Makefile.in, poly/TODO, poly/balance.c,
poly/companion.c, poly/dd.c, poly/eval.c, poly/gsl_poly.h, poly/qr.c,
poly/solve_cubic.c, poly/solve_quadratic.c, poly/test.c,
poly/zsolve.c, poly/zsolve_cubic.c, poly/zsolve_init.c,
poly/zsolve_quadratic.c, qrng/ChangeLog, qrng/Makefile.am,
qrng/Makefile.in, qrng/TODO, qrng/gsl_qrng.h, qrng/niederreiter-2.c,
qrng/qrng.c, qrng/sobol.c, qrng/test.c, randist/ChangeLog,
randist/Makefile.am, randist/Makefile.in, randist/TODO,
randist/bernoulli.c, randist/beta.c, randist/bigauss.c,
randist/binomial.c, randist/binomial_tpe.c, randist/cauchy.c,
randist/chisq.c, randist/dirichlet.c, randist/discrete.c,
randist/erlang.c, randist/exponential.c, randist/exppow.c,
randist/fdist.c, randist/flat.c, randist/gamma.c, randist/gauss.c,
randist/gausstail.c, randist/gausszig.c, randist/geometric.c,
randist/gsl_randist.h, randist/gumbel.c, randist/hyperg.c,
randist/landau.c, randist/laplace.c, randist/levy.c,
randist/logarithmic.c, randist/logistic.c, randist/lognormal.c,
randist/multinomial.c, randist/nbinomial.c, randist/pareto.c,
randist/pascal.c, randist/poisson.c, randist/rayleigh.c,
randist/shuffle.c, randist/sphere.c, randist/tdist.c, randist/test.c,
randist/weibull.c, rng/ChangeLog, rng/Makefile.am, rng/Makefile.in,
rng/TODO, rng/borosh13.c, rng/cmrg.c, rng/coveyou.c, rng/default.c,
rng/file.c, rng/fishman18.c, rng/fishman20.c, rng/fishman2x.c,
rng/gfsr4.c, rng/gsl_rng.h, rng/knuthran.c, rng/knuthran2.c,
rng/knuthran2002.c, rng/lecuyer21.c, rng/minstd.c, rng/mrg.c,
rng/mt.c, rng/r250.c, rng/ran0.c, rng/ran1.c, rng/ran2.c, rng/ran3.c,
rng/rand.c, rng/rand48.c, rng/random.c, rng/randu.c, rng/ranf.c,
rng/ranlux.c, rng/ranlxd.c, rng/ranlxs.c, rng/ranmar.c, rng/rng.c,
rng/schrage.c, rng/slatec.c, rng/taus.c, rng/taus113.c, rng/test.c,
rng/transputer.c, rng/tt.c, rng/types.c, rng/uni.c, rng/uni32.c,
rng/vax.c, rng/waterman14.c, rng/zuf.c, roots/ChangeLog,
roots/Makefile.am, roots/Makefile.in, roots/TODO, roots/bisection.c,
roots/brent.c, roots/convergence.c, roots/falsepos.c,
roots/fdfsolver.c, roots/fsolver.c, roots/gsl_roots.h,
roots/newton.c, roots/roots.h, roots/secant.c, roots/steffenson.c,
roots/test.c, roots/test.h, roots/test_funcs.c, siman/ChangeLog,
siman/Makefile.am, siman/Makefile.in, siman/TODO, siman/gsl_siman.h,
siman/siman.c, siman/siman_test_driver.sh, siman/siman_tsp.c,
siman/test.c, sort/ChangeLog, sort/Makefile.am, sort/Makefile.in,
sort/TODO, sort/gsl_heapsort.h, sort/gsl_sort.h,
sort/gsl_sort_char.h, sort/gsl_sort_double.h, sort/gsl_sort_float.h,
sort/gsl_sort_int.h, sort/gsl_sort_long.h,
sort/gsl_sort_long_double.h, sort/gsl_sort_short.h,
sort/gsl_sort_uchar.h, sort/gsl_sort_uint.h, sort/gsl_sort_ulong.h,
sort/gsl_sort_ushort.h, sort/gsl_sort_vector.h,
sort/gsl_sort_vector_char.h, sort/gsl_sort_vector_double.h,
sort/gsl_sort_vector_float.h, sort/gsl_sort_vector_int.h,
sort/gsl_sort_vector_long.h, sort/gsl_sort_vector_long_double.h,
sort/gsl_sort_vector_short.h, sort/gsl_sort_vector_uchar.h,
sort/gsl_sort_vector_uint.h, sort/gsl_sort_vector_ulong.h,
sort/gsl_sort_vector_ushort.h, sort/sort.c, sort/sortind.c,
sort/sortvec.c, sort/sortvec_source.c, sort/sortvecind.c,
sort/sortvecind_source.c, sort/subset.c, sort/subset_source.c,
sort/subsetind.c, sort/subsetind_source.c, sort/test.c,
sort/test_heapsort.c, sort/test_source.c, specfunc/ChangeLog,
specfunc/Makefile.am, specfunc/Makefile.in, specfunc/TODO,
specfunc/airy.c, specfunc/airy_der.c, specfunc/airy_zero.c,
specfunc/atanint.c, specfunc/bessel.c, specfunc/bessel.h,
specfunc/bessel_I0.c, specfunc/bessel_I1.c, specfunc/bessel_In.c,
specfunc/bessel_Inu.c, specfunc/bessel_J0.c, specfunc/bessel_J1.c,
specfunc/bessel_Jn.c, specfunc/bessel_Jnu.c, specfunc/bessel_K0.c,
specfunc/bessel_K1.c, specfunc/bessel_Kn.c, specfunc/bessel_Knu.c,
specfunc/bessel_Y0.c, specfunc/bessel_Y1.c, specfunc/bessel_Yn.c,
specfunc/bessel_Ynu.c, specfunc/bessel_amp_phase.c,
specfunc/bessel_amp_phase.h, specfunc/bessel_i.c,
specfunc/bessel_j.c, specfunc/bessel_k.c, specfunc/bessel_olver.c,
specfunc/bessel_olver.h, specfunc/bessel_sequence.c,
specfunc/bessel_temme.c, specfunc/bessel_temme.h,
specfunc/bessel_y.c, specfunc/bessel_zero.c, specfunc/beta.c,
specfunc/beta_inc.c, specfunc/cheb_eval.c, specfunc/cheb_eval_mode.c,
specfunc/chebyshev.h, specfunc/check.h, specfunc/clausen.c,
specfunc/coulomb.c, specfunc/coulomb_bound.c, specfunc/coupling.c,
specfunc/dawson.c, specfunc/debye.c, specfunc/dilog.c,
specfunc/elementary.c, specfunc/ellint.c, specfunc/elljac.c,
specfunc/erfc.c, specfunc/error.h, specfunc/eval.h, specfunc/exp.c,
specfunc/expint.c, specfunc/expint3.c, specfunc/fermi_dirac.c,
specfunc/gamma.c, specfunc/gamma_inc.c, specfunc/gegenbauer.c,
specfunc/gsl_sf.h, specfunc/gsl_sf_airy.h, specfunc/gsl_sf_bessel.h,
specfunc/gsl_sf_clausen.h, specfunc/gsl_sf_coulomb.h,
specfunc/gsl_sf_coupling.h, specfunc/gsl_sf_dawson.h,
specfunc/gsl_sf_debye.h, specfunc/gsl_sf_dilog.h,
specfunc/gsl_sf_elementary.h, specfunc/gsl_sf_ellint.h,
specfunc/gsl_sf_elljac.h, specfunc/gsl_sf_erf.h,
specfunc/gsl_sf_exp.h, specfunc/gsl_sf_expint.h,
specfunc/gsl_sf_fermi_dirac.h, specfunc/gsl_sf_gamma.h,
specfunc/gsl_sf_gegenbauer.h, specfunc/gsl_sf_hyperg.h,
specfunc/gsl_sf_laguerre.h, specfunc/gsl_sf_lambert.h,
specfunc/gsl_sf_legendre.h, specfunc/gsl_sf_log.h,
specfunc/gsl_sf_mathieu.h, specfunc/gsl_sf_pow_int.h,
specfunc/gsl_sf_psi.h, specfunc/gsl_sf_result.h,
specfunc/gsl_sf_synchrotron.h, specfunc/gsl_sf_transport.h,
specfunc/gsl_sf_trig.h, specfunc/gsl_sf_zeta.h,
specfunc/gsl_specfunc.h, specfunc/hyperg.c, specfunc/hyperg.h,
specfunc/hyperg_0F1.c, specfunc/hyperg_1F1.c, specfunc/hyperg_2F0.c,
specfunc/hyperg_2F1.c, specfunc/hyperg_U.c, specfunc/laguerre.c,
specfunc/lambert.c, specfunc/legendre.h, specfunc/legendre_H3d.c,
specfunc/legendre_Qn.c, specfunc/legendre_con.c,
specfunc/legendre_poly.c, specfunc/log.c, specfunc/mathieu_angfunc.c,
specfunc/mathieu_charv.c, specfunc/mathieu_coeff.c,
specfunc/mathieu_radfunc.c, specfunc/mathieu_workspace.c,
specfunc/poch.c, specfunc/pow_int.c, specfunc/psi.c,
specfunc/recurse.h, specfunc/result.c, specfunc/shint.c,
specfunc/sinint.c, specfunc/synchrotron.c, specfunc/test_airy.c,
specfunc/test_bessel.c, specfunc/test_coulomb.c,
specfunc/test_dilog.c, specfunc/test_gamma.c, specfunc/test_hyperg.c,
specfunc/test_legendre.c, specfunc/test_mathieu.c,
specfunc/test_sf.c, specfunc/test_sf.h, specfunc/transport.c,
specfunc/trig.c, specfunc/zeta.c, statistics/ChangeLog,
statistics/Makefile.am, statistics/Makefile.in, statistics/TODO,
statistics/absdev.c, statistics/absdev_source.c,
statistics/covariance.c, statistics/covariance_source.c,
statistics/gsl_statistics.h, statistics/gsl_statistics_char.h,
statistics/gsl_statistics_double.h,
statistics/gsl_statistics_float.h, statistics/gsl_statistics_int.h,
statistics/gsl_statistics_long.h,
statistics/gsl_statistics_long_double.h,
statistics/gsl_statistics_short.h, statistics/gsl_statistics_uchar.h,
statistics/gsl_statistics_uint.h, statistics/gsl_statistics_ulong.h,
statistics/gsl_statistics_ushort.h, statistics/kurtosis.c,
statistics/kurtosis_source.c, statistics/lag1.c,
statistics/lag1_source.c, statistics/mean.c,
statistics/mean_source.c, statistics/median.c,
statistics/median_source.c, statistics/minmax.c,
statistics/minmax_source.c, statistics/p_variance.c,
statistics/p_variance_source.c, statistics/quantiles.c,
statistics/quantiles_source.c, statistics/skew.c,
statistics/skew_source.c, statistics/test.c,
statistics/test_float_source.c, statistics/test_int_source.c,
statistics/test_nist.c, statistics/ttest.c,
statistics/ttest_source.c, statistics/variance.c,
statistics/variance_source.c, statistics/wabsdev.c,
statistics/wabsdev_source.c, statistics/wkurtosis.c,
statistics/wkurtosis_source.c, statistics/wmean.c,
statistics/wmean_source.c, statistics/wskew.c,
statistics/wskew_source.c, statistics/wvariance.c,
statistics/wvariance_source.c, sum/ChangeLog, sum/Makefile.am,
sum/Makefile.in, sum/gsl_sum.h, sum/levin_u.c, sum/levin_utrunc.c,
sum/test.c, sum/work_u.c, sum/work_utrunc.c, sys/ChangeLog,
sys/Makefile.am, sys/Makefile.in, sys/coerce.c, sys/expm1.c,
sys/fcmp.c, sys/fdiv.c, sys/gsl_sys.h, sys/hypot.c, sys/infnan.c,
sys/invhyp.c, sys/ldfrexp.c, sys/log1p.c, sys/minmax.c,
sys/pow_int.c, sys/prec.c, sys/test.c, test/ChangeLog,
test/Makefile.am, test/Makefile.in, test/gsl_test.h, test/results.c,
utils/Makefile.am, utils/Makefile.in, utils/README, utils/memcpy.c,
utils/memmove.c, utils/placeholder.c, utils/strdup.c, utils/strtol.c,
utils/strtoul.c, utils/system.h, vector/ChangeLog,
vector/Makefile.am, vector/Makefile.in, vector/TODO, vector/copy.c,
vector/copy_source.c, vector/file.c, vector/file_source.c,
vector/gsl_vector.h, vector/gsl_vector_char.h,
vector/gsl_vector_complex.h, vector/gsl_vector_complex_double.h,
vector/gsl_vector_complex_float.h,
vector/gsl_vector_complex_long_double.h, vector/gsl_vector_double.h,
vector/gsl_vector_float.h, vector/gsl_vector_int.h,
vector/gsl_vector_long.h, vector/gsl_vector_long_double.h,
vector/gsl_vector_short.h, vector/gsl_vector_uchar.h,
vector/gsl_vector_uint.h, vector/gsl_vector_ulong.h,
vector/gsl_vector_ushort.h, vector/init.c, vector/init_source.c,
vector/minmax.c, vector/minmax_source.c, vector/oper.c,
vector/oper_source.c, vector/prop.c, vector/prop_source.c,
vector/reim.c, vector/reim_source.c, vector/subvector.c,
vector/subvector_source.c, vector/swap.c, vector/swap_source.c,
vector/test.c, vector/test_complex_source.c, vector/test_source.c,
vector/test_static.c, vector/vector.c, vector/vector_source.c,
vector/view.c, vector/view.h, vector/view_source.c,
wavelet/ChangeLog, wavelet/Makefile.am, wavelet/Makefile.in,
wavelet/TODO, wavelet/bspline.c, wavelet/daubechies.c, wavelet/dwt.c,
wavelet/gsl_wavelet.h, wavelet/gsl_wavelet2d.h, wavelet/haar.c,
wavelet/test.c, wavelet/wavelet.c: New files.
Diffstat (limited to 'gsl-1.9/doc/statistics.texi')
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1 files changed, 741 insertions, 0 deletions
diff --git a/gsl-1.9/doc/statistics.texi b/gsl-1.9/doc/statistics.texi new file mode 100644 index 0000000..c289278 --- /dev/null +++ b/gsl-1.9/doc/statistics.texi @@ -0,0 +1,741 @@ +@cindex statistics +@cindex mean +@cindex standard deviation +@cindex variance +@cindex estimated standard deviation +@cindex estimated variance +@cindex t-test +@cindex range +@cindex min +@cindex max + +This chapter describes the statistical functions in the library. The +basic statistical functions include routines to compute the mean, +variance and standard deviation. More advanced functions allow you to +calculate absolute deviations, skewness, and kurtosis as well as the +median and arbitrary percentiles. The algorithms use recurrence +relations to compute average quantities in a stable way, without large +intermediate values that might overflow. + +The functions are available in versions for datasets in the standard +floating-point and integer types. The versions for double precision +floating-point data have the prefix @code{gsl_stats} and are declared in +the header file @file{gsl_statistics_double.h}. The versions for integer +data have the prefix @code{gsl_stats_int} and are declared in the header +file @file{gsl_statistics_int.h}. + +@menu +* Mean and standard deviation and variance:: +* Absolute deviation:: +* Higher moments (skewness and kurtosis):: +* Autocorrelation:: +* Covariance:: +* Weighted Samples:: +* Maximum and Minimum values:: +* Median and Percentiles:: +* Example statistical programs:: +* Statistics References and Further Reading:: +@end menu + +@node Mean and standard deviation and variance +@section Mean, Standard Deviation and Variance + +@deftypefun double gsl_stats_mean (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the arithmetic mean of @var{data}, a dataset of +length @var{n} with stride @var{stride}. The arithmetic mean, or +@dfn{sample mean}, is denoted by @math{\Hat\mu} and defined as, +@tex +\beforedisplay +$$ +{\Hat\mu} = {1 \over N} \sum x_i +$$ +\afterdisplay +@end tex +@ifinfo + +@example +\Hat\mu = (1/N) \sum x_i +@end example + +@end ifinfo +@noindent +where @math{x_i} are the elements of the dataset @var{data}. For +samples drawn from a gaussian distribution the variance of +@math{\Hat\mu} is @math{\sigma^2 / N}. +@end deftypefun + +@deftypefun double gsl_stats_variance (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the estimated, or @dfn{sample}, variance of +@var{data}, a dataset of length @var{n} with stride @var{stride}. The +estimated variance is denoted by @math{\Hat\sigma^2} and is defined by, +@tex +\beforedisplay +$$ +{\Hat\sigma}^2 = {1 \over (N-1)} \sum (x_i - {\Hat\mu})^2 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +\Hat\sigma^2 = (1/(N-1)) \sum (x_i - \Hat\mu)^2 +@end example + +@end ifinfo +@noindent +where @math{x_i} are the elements of the dataset @var{data}. Note that +the normalization factor of @math{1/(N-1)} results from the derivation +of @math{\Hat\sigma^2} as an unbiased estimator of the population +variance @math{\sigma^2}. For samples drawn from a gaussian distribution +the variance of @math{\Hat\sigma^2} itself is @math{2 \sigma^4 / N}. + +This function computes the mean via a call to @code{gsl_stats_mean}. If +you have already computed the mean then you can pass it directly to +@code{gsl_stats_variance_m}. +@end deftypefun + +@deftypefun double gsl_stats_variance_m (const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{mean}) +This function returns the sample variance of @var{data} relative to the +given value of @var{mean}. The function is computed with @math{\Hat\mu} +replaced by the value of @var{mean} that you supply, +@tex +\beforedisplay +$$ +{\Hat\sigma}^2 = {1 \over (N-1)} \sum (x_i - mean)^2 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +\Hat\sigma^2 = (1/(N-1)) \sum (x_i - mean)^2 +@end example +@end ifinfo +@end deftypefun + +@deftypefun double gsl_stats_sd (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +@deftypefunx double gsl_stats_sd_m (const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{mean}) +The standard deviation is defined as the square root of the variance. +These functions return the square root of the corresponding variance +functions above. +@end deftypefun + +@deftypefun double gsl_stats_variance_with_fixed_mean (const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{mean}) +This function computes an unbiased estimate of the variance of +@var{data} when the population mean @var{mean} of the underlying +distribution is known @emph{a priori}. In this case the estimator for +the variance uses the factor @math{1/N} and the sample mean +@math{\Hat\mu} is replaced by the known population mean @math{\mu}, +@tex +\beforedisplay +$$ +{\Hat\sigma}^2 = {1 \over N} \sum (x_i - \mu)^2 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +\Hat\sigma^2 = (1/N) \sum (x_i - \mu)^2 +@end example +@end ifinfo +@end deftypefun + + +@deftypefun double gsl_stats_sd_with_fixed_mean (const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{mean}) +This function calculates the standard deviation of @var{data} for a +fixed population mean @var{mean}. The result is the square root of the +corresponding variance function. +@end deftypefun + +@node Absolute deviation +@section Absolute deviation + +@deftypefun double gsl_stats_absdev (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function computes the absolute deviation from the mean of +@var{data}, a dataset of length @var{n} with stride @var{stride}. The +absolute deviation from the mean is defined as, +@tex +\beforedisplay +$$ +absdev = {1 \over N} \sum |x_i - {\Hat\mu}| +$$ +\afterdisplay +@end tex +@ifinfo + +@example +absdev = (1/N) \sum |x_i - \Hat\mu| +@end example + +@end ifinfo +@noindent +where @math{x_i} are the elements of the dataset @var{data}. The +absolute deviation from the mean provides a more robust measure of the +width of a distribution than the variance. This function computes the +mean of @var{data} via a call to @code{gsl_stats_mean}. +@end deftypefun + +@deftypefun double gsl_stats_absdev_m (const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{mean}) +This function computes the absolute deviation of the dataset @var{data} +relative to the given value of @var{mean}, +@tex +\beforedisplay +$$ +absdev = {1 \over N} \sum |x_i - mean| +$$ +\afterdisplay +@end tex +@ifinfo + +@example +absdev = (1/N) \sum |x_i - mean| +@end example + +@end ifinfo +@noindent +This function is useful if you have already computed the mean of +@var{data} (and want to avoid recomputing it), or wish to calculate the +absolute deviation relative to another value (such as zero, or the +median). +@end deftypefun + +@node Higher moments (skewness and kurtosis) +@section Higher moments (skewness and kurtosis) + +@deftypefun double gsl_stats_skew (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function computes the skewness of @var{data}, a dataset of length +@var{n} with stride @var{stride}. The skewness is defined as, +@tex +\beforedisplay +$$ +skew = {1 \over N} \sum + {\left( x_i - {\Hat\mu} \over {\Hat\sigma} \right)}^3 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +skew = (1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^3 +@end example + +@end ifinfo +@noindent +where @math{x_i} are the elements of the dataset @var{data}. The skewness +measures the asymmetry of the tails of a distribution. + +The function computes the mean and estimated standard deviation of +@var{data} via calls to @code{gsl_stats_mean} and @code{gsl_stats_sd}. +@end deftypefun + +@deftypefun double gsl_stats_skew_m_sd (const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{mean}, double @var{sd}) +This function computes the skewness of the dataset @var{data} using the +given values of the mean @var{mean} and standard deviation @var{sd}, +@tex +\beforedisplay +$$ +skew = {1 \over N} + \sum {\left( x_i - mean \over sd \right)}^3 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +skew = (1/N) \sum ((x_i - mean)/sd)^3 +@end example + +@end ifinfo +@noindent +These functions are useful if you have already computed the mean and +standard deviation of @var{data} and want to avoid recomputing them. +@end deftypefun + +@deftypefun double gsl_stats_kurtosis (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function computes the kurtosis of @var{data}, a dataset of length +@var{n} with stride @var{stride}. The kurtosis is defined as, +@tex +\beforedisplay +$$ +kurtosis = \left( {1 \over N} \sum + {\left(x_i - {\Hat\mu} \over {\Hat\sigma} \right)}^4 + \right) + - 3 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +kurtosis = ((1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^4) - 3 +@end example + +@end ifinfo +@noindent +The kurtosis measures how sharply peaked a distribution is, relative to +its width. The kurtosis is normalized to zero for a gaussian +distribution. +@end deftypefun + +@deftypefun double gsl_stats_kurtosis_m_sd (const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{mean}, double @var{sd}) +This function computes the kurtosis of the dataset @var{data} using the +given values of the mean @var{mean} and standard deviation @var{sd}, +@tex +\beforedisplay +$$ +kurtosis = {1 \over N} + \left( \sum {\left(x_i - mean \over sd \right)}^4 \right) + - 3 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +kurtosis = ((1/N) \sum ((x_i - mean)/sd)^4) - 3 +@end example + +@end ifinfo +@noindent +This function is useful if you have already computed the mean and +standard deviation of @var{data} and want to avoid recomputing them. +@end deftypefun + +@node Autocorrelation +@section Autocorrelation + +@deftypefun double gsl_stats_lag1_autocorrelation (const double @var{data}[], const size_t @var{stride}, const size_t @var{n}) +This function computes the lag-1 autocorrelation of the dataset @var{data}. +@tex +\beforedisplay +$$ +a_1 = {\sum_{i = 1}^{n} (x_{i} - \Hat\mu) (x_{i-1} - \Hat\mu) +\over +\sum_{i = 1}^{n} (x_{i} - \Hat\mu) (x_{i} - \Hat\mu)} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +a_1 = @{\sum_@{i = 1@}^@{n@} (x_@{i@} - \Hat\mu) (x_@{i-1@} - \Hat\mu) + \over + \sum_@{i = 1@}^@{n@} (x_@{i@} - \Hat\mu) (x_@{i@} - \Hat\mu)@} +@end example +@end ifinfo +@end deftypefun + + +@deftypefun double gsl_stats_lag1_autocorrelation_m (const double @var{data}[], const size_t @var{stride}, const size_t @var{n}, const double @var{mean}) +This function computes the lag-1 autocorrelation of the dataset +@var{data} using the given value of the mean @var{mean}. + +@end deftypefun + +@node Covariance +@section Covariance +@cindex covariance, of two datasets + +@deftypefun double gsl_stats_covariance (const double @var{data1}[], const size_t @var{stride1}, const double @var{data2}[], const size_t @var{stride2}, const size_t @var{n}) +This function computes the covariance of the datasets @var{data1} and +@var{data2} which must both be of the same length @var{n}. +@tex +\beforedisplay +$$ +covar = {1 \over (n - 1)} \sum_{i = 1}^{n} (x_{i} - \Hat x) (y_{i} - \Hat y) +$$ +\afterdisplay +@end tex +@ifinfo + +@example +covar = (1/(n - 1)) \sum_@{i = 1@}^@{n@} (x_i - \Hat x) (y_i - \Hat y) +@end example +@end ifinfo +@end deftypefun + +@deftypefun double gsl_stats_covariance_m (const double @var{data1}[], const size_t @var{stride1}, const double @var{data2}[], const size_t @var{stride2}, const size_t @var{n}, const double @var{mean1}, const double @var{mean2}) +This function computes the covariance of the datasets @var{data1} and +@var{data2} using the given values of the means, @var{mean1} and +@var{mean2}. This is useful if you have already computed the means of +@var{data1} and @var{data2} and want to avoid recomputing them. +@end deftypefun + + +@node Weighted Samples +@section Weighted Samples + +The functions described in this section allow the computation of +statistics for weighted samples. The functions accept an array of +samples, @math{x_i}, with associated weights, @math{w_i}. Each sample +@math{x_i} is considered as having been drawn from a Gaussian +distribution with variance @math{\sigma_i^2}. The sample weight +@math{w_i} is defined as the reciprocal of this variance, @math{w_i = +1/\sigma_i^2}. Setting a weight to zero corresponds to removing a +sample from a dataset. + +@deftypefun double gsl_stats_wmean (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the weighted mean of the dataset @var{data} with +stride @var{stride} and length @var{n}, using the set of weights @var{w} +with stride @var{wstride} and length @var{n}. The weighted mean is defined as, +@tex +\beforedisplay +$$ +{\Hat\mu} = {{\sum w_i x_i} \over {\sum w_i}} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +\Hat\mu = (\sum w_i x_i) / (\sum w_i) +@end example +@end ifinfo +@end deftypefun + + +@deftypefun double gsl_stats_wvariance (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the estimated variance of the dataset @var{data} +with stride @var{stride} and length @var{n}, using the set of weights +@var{w} with stride @var{wstride} and length @var{n}. The estimated +variance of a weighted dataset is defined as, +@tex +\beforedisplay +$$ +\Hat\sigma^2 = {{\sum w_i} \over {(\sum w_i)^2 - \sum (w_i^2)}} + \sum w_i (x_i - \Hat\mu)^2 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +\Hat\sigma^2 = ((\sum w_i)/((\sum w_i)^2 - \sum (w_i^2))) + \sum w_i (x_i - \Hat\mu)^2 +@end example + +@end ifinfo +@noindent +Note that this expression reduces to an unweighted variance with the +familiar @math{1/(N-1)} factor when there are @math{N} equal non-zero +weights. +@end deftypefun + +@deftypefun double gsl_stats_wvariance_m (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{wmean}) +This function returns the estimated variance of the weighted dataset +@var{data} using the given weighted mean @var{wmean}. +@end deftypefun + +@deftypefun double gsl_stats_wsd (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}) +The standard deviation is defined as the square root of the variance. +This function returns the square root of the corresponding variance +function @code{gsl_stats_wvariance} above. +@end deftypefun + +@deftypefun double gsl_stats_wsd_m (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{wmean}) +This function returns the square root of the corresponding variance +function @code{gsl_stats_wvariance_m} above. +@end deftypefun + +@deftypefun double gsl_stats_wvariance_with_fixed_mean (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}, const double @var{mean}) +This function computes an unbiased estimate of the variance of weighted +dataset @var{data} when the population mean @var{mean} of the underlying +distribution is known @emph{a priori}. In this case the estimator for +the variance replaces the sample mean @math{\Hat\mu} by the known +population mean @math{\mu}, +@tex +\beforedisplay +$$ +\Hat\sigma^2 = {{\sum w_i (x_i - \mu)^2} \over {\sum w_i}} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +\Hat\sigma^2 = (\sum w_i (x_i - \mu)^2) / (\sum w_i) +@end example +@end ifinfo +@end deftypefun + +@deftypefun double gsl_stats_wsd_with_fixed_mean (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}, const double @var{mean}) +The standard deviation is defined as the square root of the variance. +This function returns the square root of the corresponding variance +function above. +@end deftypefun + +@deftypefun double gsl_stats_wabsdev (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function computes the weighted absolute deviation from the weighted +mean of @var{data}. The absolute deviation from the mean is defined as, +@tex +\beforedisplay +$$ +absdev = {{\sum w_i |x_i - \Hat\mu|} \over {\sum w_i}} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +absdev = (\sum w_i |x_i - \Hat\mu|) / (\sum w_i) +@end example +@end ifinfo +@end deftypefun + +@deftypefun double gsl_stats_wabsdev_m (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{wmean}) +This function computes the absolute deviation of the weighted dataset +@var{data} about the given weighted mean @var{wmean}. +@end deftypefun + +@deftypefun double gsl_stats_wskew (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function computes the weighted skewness of the dataset @var{data}. +@tex +\beforedisplay +$$ +skew = {{\sum w_i ((x_i - xbar)/\sigma)^3} \over {\sum w_i}} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +skew = (\sum w_i ((x_i - xbar)/\sigma)^3) / (\sum w_i) +@end example +@end ifinfo +@end deftypefun + +@deftypefun double gsl_stats_wskew_m_sd (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{wmean}, double @var{wsd}) +This function computes the weighted skewness of the dataset @var{data} +using the given values of the weighted mean and weighted standard +deviation, @var{wmean} and @var{wsd}. +@end deftypefun + +@deftypefun double gsl_stats_wkurtosis (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function computes the weighted kurtosis of the dataset @var{data}. + +@tex +\beforedisplay +$$ +kurtosis = {{\sum w_i ((x_i - xbar)/sigma)^4} \over {\sum w_i}} - 3 +$$ +\afterdisplay +@end tex +@ifinfo + +@example +kurtosis = ((\sum w_i ((x_i - xbar)/sigma)^4) / (\sum w_i)) - 3 +@end example +@end ifinfo +@end deftypefun + +@deftypefun double gsl_stats_wkurtosis_m_sd (const double @var{w}[], size_t @var{wstride}, const double @var{data}[], size_t @var{stride}, size_t @var{n}, double @var{wmean}, double @var{wsd}) +This function computes the weighted kurtosis of the dataset @var{data} +using the given values of the weighted mean and weighted standard +deviation, @var{wmean} and @var{wsd}. +@end deftypefun + +@node Maximum and Minimum values +@section Maximum and Minimum values + +The following functions find the maximum and minimum values of a +dataset (or their indices). If the data contains @code{NaN}s then a +@code{NaN} will be returned, since the maximum or minimum value is +undefined. For functions which return an index, the location of the +first @code{NaN} in the array is returned. + +@deftypefun double gsl_stats_max (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the maximum value in @var{data}, a dataset of +length @var{n} with stride @var{stride}. The maximum value is defined +as the value of the element @math{x_i} which satisfies @c{$x_i \ge x_j$} +@math{x_i >= x_j} for all @math{j}. + +If you want instead to find the element with the largest absolute +magnitude you will need to apply @code{fabs} or @code{abs} to your data +before calling this function. +@end deftypefun + +@deftypefun double gsl_stats_min (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the minimum value in @var{data}, a dataset of +length @var{n} with stride @var{stride}. The minimum value is defined +as the value of the element @math{x_i} which satisfies @c{$x_i \le x_j$} +@math{x_i <= x_j} for all @math{j}. + +If you want instead to find the element with the smallest absolute +magnitude you will need to apply @code{fabs} or @code{abs} to your data +before calling this function. +@end deftypefun + +@deftypefun void gsl_stats_minmax (double * @var{min}, double * @var{max}, const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function finds both the minimum and maximum values @var{min}, +@var{max} in @var{data} in a single pass. +@end deftypefun + +@deftypefun size_t gsl_stats_max_index (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the index of the maximum value in @var{data}, a +dataset of length @var{n} with stride @var{stride}. The maximum value is +defined as the value of the element @math{x_i} which satisfies +@c{$x_i \ge x_j$} +@math{x_i >= x_j} for all @math{j}. When there are several equal maximum +elements then the first one is chosen. +@end deftypefun + +@deftypefun size_t gsl_stats_min_index (const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the index of the minimum value in @var{data}, a +dataset of length @var{n} with stride @var{stride}. The minimum value +is defined as the value of the element @math{x_i} which satisfies +@c{$x_i \ge x_j$} +@math{x_i >= x_j} for all @math{j}. When there are several equal +minimum elements then the first one is chosen. +@end deftypefun + +@deftypefun void gsl_stats_minmax_index (size_t * @var{min_index}, size_t * @var{max_index}, const double @var{data}[], size_t @var{stride}, size_t @var{n}) +This function returns the indexes @var{min_index}, @var{max_index} of +the minimum and maximum values in @var{data} in a single pass. +@end deftypefun + +@node Median and Percentiles +@section Median and Percentiles + +The median and percentile functions described in this section operate on +sorted data. For convenience we use @dfn{quantiles}, measured on a scale +of 0 to 1, instead of percentiles (which use a scale of 0 to 100). + +@deftypefun double gsl_stats_median_from_sorted_data (const double @var{sorted_data}[], size_t @var{stride}, size_t @var{n}) +This function returns the median value of @var{sorted_data}, a dataset +of length @var{n} with stride @var{stride}. The elements of the array +must be in ascending numerical order. There are no checks to see +whether the data are sorted, so the function @code{gsl_sort} should +always be used first. + +When the dataset has an odd number of elements the median is the value +of element @math{(n-1)/2}. When the dataset has an even number of +elements the median is the mean of the two nearest middle values, +elements @math{(n-1)/2} and @math{n/2}. Since the algorithm for +computing the median involves interpolation this function always returns +a floating-point number, even for integer data types. +@end deftypefun + +@deftypefun double gsl_stats_quantile_from_sorted_data (const double @var{sorted_data}[], size_t @var{stride}, size_t @var{n}, double @var{f}) +This function returns a quantile value of @var{sorted_data}, a +double-precision array of length @var{n} with stride @var{stride}. The +elements of the array must be in ascending numerical order. The +quantile is determined by the @var{f}, a fraction between 0 and 1. For +example, to compute the value of the 75th percentile @var{f} should have +the value 0.75. + +There are no checks to see whether the data are sorted, so the function +@code{gsl_sort} should always be used first. + +The quantile is found by interpolation, using the formula +@tex +\beforedisplay +$$ +\hbox{quantile} = (1 - \delta) x_i + \delta x_{i+1} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +quantile = (1 - \delta) x_i + \delta x_@{i+1@} +@end example + +@end ifinfo +@noindent +where @math{i} is @code{floor}(@math{(n - 1)f}) and @math{\delta} is +@math{(n-1)f - i}. + +Thus the minimum value of the array (@code{data[0*stride]}) is given by +@var{f} equal to zero, the maximum value (@code{data[(n-1)*stride]}) is +given by @var{f} equal to one and the median value is given by @var{f} +equal to 0.5. Since the algorithm for computing quantiles involves +interpolation this function always returns a floating-point number, even +for integer data types. +@end deftypefun + + +@comment @node Statistical tests +@comment @section Statistical tests + +@comment FIXME, do more work on the statistical tests + +@comment -@deftypefun double gsl_stats_ttest (const double @var{data1}[], double @var{data2}[], size_t @var{n1}, size_t @var{n2}) +@comment -@deftypefunx Statistics double gsl_stats_int_ttest (const double @var{data1}[], double @var{data2}[], size_t @var{n1}, size_t @var{n2}) + +@comment The function @code{gsl_stats_ttest} computes the t-test statistic for +@comment the two arrays @var{data1}[] and @var{data2}[], of lengths @var{n1} and +@comment -@var{n2} respectively. + +@comment The t-test statistic measures the difference between the means of two +@comment datasets. + +@node Example statistical programs +@section Examples +Here is a basic example of how to use the statistical functions: + +@example +@verbatiminclude examples/stat.c +@end example + +The program should produce the following output, + +@example +@verbatiminclude examples/stat.out +@end example + + +Here is an example using sorted data, + +@example +@verbatiminclude examples/statsort.c +@end example + +This program should produce the following output, + +@example +@verbatiminclude examples/statsort.out +@end example + +@node Statistics References and Further Reading +@section References and Further Reading + +The standard reference for almost any topic in statistics is the +multi-volume @cite{Advanced Theory of Statistics} by Kendall and Stuart. + +@itemize @asis +@item +Maurice Kendall, Alan Stuart, and J. Keith Ord. +@cite{The Advanced Theory of Statistics} (multiple volumes) +reprinted as @cite{Kendall's Advanced Theory of Statistics}. +Wiley, ISBN 047023380X. +@end itemize + +@noindent +Many statistical concepts can be more easily understood by a Bayesian +approach. The following book by Gelman, Carlin, Stern and Rubin gives a +comprehensive coverage of the subject. + +@itemize @asis +@item +Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin. +@cite{Bayesian Data Analysis}. +Chapman & Hall, ISBN 0412039915. +@end itemize + +@noindent +For physicists the Particle Data Group provides useful reviews of +Probability and Statistics in the ``Mathematical Tools'' section of its +Annual Review of Particle Physics. + +@itemize @asis +@item +@cite{Review of Particle Properties} +R.M. Barnett et al., Physical Review D54, 1 (1996) +@end itemize + +@noindent +The Review of Particle Physics is available online at +the website @uref{http://pdg.lbl.gov/}. + + |