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## Re: why there are multiple functions for CDF of beta distribution?

 From: Vasu Jaganath Subject: Re: why there are multiple functions for CDF of beta distribution? Date: Thu, 9 Jan 2020 18:30:18 -0700

```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 <address@hidden>
wrote:

> Thanks Martin,
>
> I will test it out.
>
> On Tue, Jan 7, 2020 at 11:16 PM Martin Jansche <address@hidden> 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 <address@hidden>
>> 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
>>>
>>
```

gsl_invBeta.c
Description: Text Data

scipy_invBeta.py
Description: Text Data