Incorrect binomial cumulative distribution function results

[MetaEntropy]

On the HP Prime (firmware version 2016 12 08 (11226)) the binomial_cdf function gives incorrect results for values close to zero.

Steps to reproduce : In the HOME screen, type

BINOMIAL_CDF(100,0.5,1)*10^12

Observed result : 1

Expected result : 7.967*10^-17

Details : BINOMIAL_CDF seems to be rounded up to 10^-12 when it's below 10^-12, except for a number of successes k=0

This bug seems to affect the HP 39gII too.

[Tim_Wessman]

Thank you for finding this subtle issue! It was actually in the very extremes of the incomplete beta function. This was later used to implement binomial_cdf and created the problem in these rare cases.

In the meantime, you can use "binomial_cdf" in the CAS screen and you will get the correct result. Thanks again!

[MetaEntropy]

Thanks for your quick reply.

The CAS system is not exact either, maybe because it is based on too large fractions.

exact(BINOMIAL_CDF(100,1/2,21)) returns 1/461041954.

I'm not sure this is exact. 1/461041954 equals to 2.16900000e-9 while the R statistical software finds 2.168683e-09 in two different ways (sum of probability mass function and cumulative distribution function).

Anyway, I would expect a huge fraction with the exact binomial distribution.

Are fractions based on floating point numerator and denominators ? Rounding errors may be worse than in the non-CAS mode.

Secondly, for n=100 and k<=20, it's always equal to zero:

exact(BINOMIAL_CDF(100,1/2,20)) returns 0

[Jan_D]

Using the command exact is not the way to do CAS calculations.

You will have to press the CAS key in order to get into CAS environment.

When I repeat the calculations you did I get a result in the form of a fraction with a huge numerator and denominator.

The result can be converted into a numerical number by pressing  Shift -Enter, which gives the result you expected.

As a check I subtracted 

BINOMIAL_CDF(100,1/2,21) - BINOMIAL_CDF(100,1/2,20)

which should give BINOMIAL(100,1/2,21), and it does.

So very probably the result is exact.

[Jan_D]

Direct check:

[MetaEntropy]

It works, indeed.

Thank you.