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best, Feng Sent from Outlook/Android. ________________________________ From: Help-gsl <help-gsl-bounces+wang_feng=live....@gnu.org> on behalf of Vasu Jaganath <vadie.develo...@gmail.com> Sent: Friday, January 10, 2020 7:48:15 PM To: Martin Jansche <mjans...@gmail.com> Cc: GSL Mailing List <help-gsl@gnu.org> Subject: Re: why there are multiple functions for CDF of beta distribution? Thanks Martin, I settled on similar approach, I use the bisection method in the betainv.c, This approach seems much cleaner, I however have some strange corner cases where a>100 and b >100, I handle them separately. I will try to benchmark both approaches with my data to see which is faster. On Fri, Jan 10, 2020 at 1:04 AM Martin Jansche <mjans...@gmail.com> wrote: > Yup, this is a problem. When I compile and run your program gsl_invBeta.c > (which should #include <gsl/gsl_cdf.h>), I get: > > Observed: > gsl: betainv.c:181: > <http://git.savannah.gnu.org/cgit/gsl.git/tree/cdf/betainv.c#n181> ERROR: > inverse failed to converge > Default GSL error handler invoked. > Abort trap: 6 > > Expected result: > 1.0 > > Result with more precision: > 0.99999999999999999999999999980178072518730245884823... > > For the supplied values of alpha and beta, the CDF rises very steeply near > 1 and the inverse CDF is equal to 1.0 within double precision when P>0.5 > (that may not be a tight bound, but is a sufficient condition). > > Generic workaround: > > #include <stdio.h> > #include <gsl/gsl_sf_gamma.h> > > // Computes the inverse function of gsl_sf_beta_inc by binary search. > double qbeta(double p, double a, double b) { > double x = 0.5; > for (double delta = 0.25; delta > 0; delta /= 2) { > const double beta_P = gsl_sf_beta_inc(a, b, x); > const double new_x = p > beta_P ? x + delta : x - delta; > if (beta_P == p || x == new_x) break; > x = new_x; > } > return x; > } > > int main() { > double a = 5.3729222; > double b = 0.018122864; > double p = 0.67276126; > > printf("%.18g\n", qbeta(p, a, b)); > > printf("%.7g (expected: 0.25)\n", qbeta(0.25, 1, 1)); > printf("%.7g (expected: 0.9922861)\n", qbeta(0.25, 5, 0.1)); > printf("%.7g (expected: 2.954261e-200)\n", qbeta(1e-50, 0.25, 0.5)); > > return 0; > } > > Hope this helps, > -- mj > > On Fri, Jan 10, 2020 at 1:30 AM Vasu Jaganath <vadie.develo...@gmail.com> > wrote: > >> Martin and others, >> >> Following up, I have a particular example for which both Q and P variants >> of inverse functions fail. >> >> where as scipy beta.ppf (equivalent to gsl_cdf_beta_Pinv) does the right >> thing and converges to 1 or nearest double. >> >> I am attaching a very simple example with exact same data, the gsl >> function fails where as scipy function does the right thing. >> >> Any thoughts? any workarounds? Maybe there is a way I can specify >> convergence criteria? >> >> Thanks, >> Vasu >> >> >> On Wed, Jan 8, 2020 at 12:42 PM Vasu Jaganath <vadie.develo...@gmail.com> >> wrote: >> >>> Thanks Martin, >>> >>> I will test it out. >>> >>> On Tue, Jan 7, 2020 at 11:16 PM Martin Jansche <mjans...@gmail.com> >>> wrote: >>> >>>> There are many more floating point values between 0.0 and 0.001 than >>>> there are between 0.999 and 1.0. The difference between 1.0 and the next >>>> smaller double value is only around 1e-16, but the next larger double value >>>> after 0.0 is about 1e-303. So beta_P(0.9, 1, 17) will be necessarily >>>> equivalent to 1.0 due to lack of precision, whereas beta_Q(0.9, 1, 17) will >>>> be 1e-17. (Haven't tried this in GSL. You may want to try and report back.) >>>> >>>> On Wed, Jan 8, 2020 at 1:35 AM Vasu Jaganath <vadie.develo...@gmail.com> >>>> wrote: >>>> >>>>> Hi all, >>>>> >>>>> This is probably a very silly question, >>>>> >>>>> I don't understand why there are two separate P and Q variants for >>>>> CDFs? >>>>> particularly for beta distribution? >>>>> >>>>> >>>>> https://www.gnu.org/software/gsl/doc/html/randist.html#the-beta-distribution >>>>> >>>>> Thanks, >>>>> Vasu >>>>> >>>>