[Scilab-users] Can Scilab compute the inverse of the regularized Incomplete Beta Function?

[Heinz Nabielek]

> On 18.05.2020, at 14:18, Dang Ngoc Chan, Christophe <Christophe.Dang at sidel.com> wrote:
> 
> Hello,
> 
>> De  Heinz Nabielek
>> Envoyé : dimanche 17 mai 2020 23:50
>> 
>> CONF=0.95; N=1432; n=1:
>> One-sided 95% upper confidence limit fraction = BETA.INV(CONF, n+1, N+1-n)
>> = 0.003306121
>> 
>> How would I do that in Scilab?
> 
> Would it be :
> 
> [X,Y]=cdfbet("XY", n+1, N+1-n, CONF, 1-CONF)
> X  =
> 
>   0.0033061


Written with more digits

0.0033061215, and EXCEL finds

0.003306121493. Very good agreement. I am glad I had asked.

And the HELP provides real support with the statement

Description
Calculates any one parameter of the beta distribution given values for the others (The beta density is proportional to t^(A-1) * (1-t)^(B-1).

Since my originating binomial distribution is obviously

	t^n  *  (1-t)^(N-n),

the parameters for the Beta Function have to be

A=n+1
B=N+1-n

to obtain an upper conficende limit fraction = Beta.Inv(CONF, n+1, N+1-n)  !!!

Textbooks write Beta.Inv(CONF, n+1, N-n) since the last 50 years and it is wrong. And "R" is also using this wrong correlation in their binom.test

Great many thanks for all the help.
Heinz

______________
Dr Heinz Nabielek
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cell +43 677 616 349 22
heinznabielek at me.com