Mercurial > hg > octave-lyh
changeset 17226:251807f3cdc1
tcdf.m: Improve accuracy around zero and add tests.
* scripts/statistics/distributions/tcdf.m: Improve accuracy around zero
and add tests.
author | Julien Bect <julien.bect@supelec.fr> |
---|---|
date | Mon, 12 Aug 2013 14:47:21 +0200 |
parents | 57680d1227ca |
children | 33ce8c381f2c |
files | scripts/statistics/distributions/tcdf.m |
diffstat | 1 files changed, 67 insertions(+), 2 deletions(-) [+] |
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--- a/scripts/statistics/distributions/tcdf.m +++ b/scripts/statistics/distributions/tcdf.m @@ -1,3 +1,4 @@ +## Copyright (C) 2013 Julien Bect ## Copyright (C) 2012 Rik Wehbring ## Copyright (C) 1995-2012 Kurt Hornik ## @@ -51,11 +52,26 @@ endif k = !isinf (x) & (n > 0); + + xx = x .^ 2; + x_big_abs = (xx > n); + + ## deal with the case "abs(x) big" + kk = k & x_big_abs; if (isscalar (n)) - cdf(k) = betainc (1 ./ (1 + x(k) .^ 2 / n), n/2, 1/2) / 2; + cdf(kk) = betainc (n ./ (n + xx(kk)), n/2, 1/2) / 2; else - cdf(k) = betainc (1 ./ (1 + x(k) .^ 2 ./ n(k)), n(k)/2, 1/2) / 2; + cdf(kk) = betainc (n(kk) ./ (n(kk) + xx(kk)), n(kk)/2, 1/2) / 2; endif + + ## deal with the case "abs(x) small" + kk = k & !x_big_abs; + if (isscalar (n)) + cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n + xx(kk)), 1/2, n/2)); + else + cdf(kk) = 0.5 * (1 - betainc (xx(kk) ./ (n(kk) + xx(kk)), 1/2, n(kk)/2)); + endif + k &= (x > 0); if (any (k(:))) cdf(k) = 1 - cdf(k); @@ -92,3 +108,52 @@ %!error tcdf (i, 2) %!error tcdf (2, i) +## Check some reference values + +%!shared tol_rel +%! tol_rel = 10 * eps; + +## check accuracy for small positive values +%!assert (tcdf (10^(-10), 2.5), 0.50000000003618087, -tol_rel) +%!assert (tcdf (10^(-11), 2.5), 0.50000000000361809, -tol_rel) +%!assert (tcdf (10^(-12), 2.5), 0.50000000000036181, -tol_rel) +%!assert (tcdf (10^(-13), 2.5), 0.50000000000003618, -tol_rel) +%!assert (tcdf (10^(-14), 2.5), 0.50000000000000362, -tol_rel) +%!assert (tcdf (10^(-15), 2.5), 0.50000000000000036, -tol_rel) +%!assert (tcdf (10^(-16), 2.5), 0.50000000000000004, -tol_rel) + +## check accuracy for large negative values +%!assert (tcdf (-10^1, 2.5), 2.2207478836537124e-03, -tol_rel) +%!assert (tcdf (-10^2, 2.5), 7.1916492116661878e-06, -tol_rel) +%!assert (tcdf (-10^3, 2.5), 2.2747463948307452e-08, -tol_rel) +%!assert (tcdf (-10^4, 2.5), 7.1933970159922115e-11, -tol_rel) +%!assert (tcdf (-10^5, 2.5), 2.2747519231756221e-13, -tol_rel) + +## # Reference values obtained using Python 2.7.4 and mpmath 0.17 +## +## from mpmath import * +## +## mp.dps = 100 +## +## def F(x_in, nu_in): +## x = mpf(x_in); +## nu = mpf(nu_in); +## t = nu / (nu + x*x) +## a = nu / 2 +## b = mpf(0.5) +## F = betainc(a, b, 0, t, regularized=True) / 2 +## if (x > 0): +## F = 1 - F +## return F +## +## nu = 2.5 +## +## for i in range(1, 6): +## x = - power(mpf(10), mpf(i)) +## print "%%!assert (tcdf (-10^%d, 2.5), %s, -eps)" \ +## % (i, nstr(F(x, nu), 17)) +## +## for i in range(10, 17): +## x = power(mpf(10), -mpf(i)) +## print "%%!assert (tcdf (10^(-%d), 2.5), %s, -eps)" \ +## % (i, nstr(F(x, nu), 17))