# Questions tagged [beta-function]

For questions about the Beta function, a special function closely related to the Gamma function. It is advisable to also use the [special-functions] tag in conjunction with this tag.

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### Solving equation involving factorials

I have this particular equation $\frac{(\alpha-1)!(\beta-1)!}{(\alpha+\beta-1)!} = \frac{\Gamma(p)(1+q)^{n+2p} 2^n}{q^{p}(2+q)^{n+p}}$. Now, given the values of $\alpha$ and $\beta$, I need to find ...
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### Analogue to the beta-binomial distribution for sampling without replacement?

The beta-binomial distribution characterizes the number of successes in $n$ trials, but where the probability of success at each trial is unknown or random. However, suppose that you had finite ...
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### Incomplete Beta function

I am looking for an approximation/bound for the incomplete Beta function $B_z(a,b)$ when $z\to0$. I know the Taylor expansion would help. However, I need a power series in $z^n$ (the exponential is an ...
Estimate the probability of success Suppose I send 10 tasks to my machine. 6 out of 10 tasks success, and 4 failed. These outcomes is summarized by $X$ as a binary variable, 1 is task success, and 0 ...