Beta Type II Distribution Calculator
Use this calculator to find the probability density and cumulative probabilities for Beta Type II distribution with parameter $\alpha$ and $\beta$.
| Beta Type II Distribution Calculator | |
|---|---|
| First Parameter $\alpha$: | |
| Second Parameter $\beta$ | |
| Value of x | |
| Results | |
| Probability density : f(x) | |
| Probability X less than x: P(X < x) | |
| Probability X greater than x: P(X > x) | |
Definition of Beta Type II Distribution
A continuous random variable $X$ is said to have a beta type II distribution with parameter $\alpha$ and $\beta$ if its p.d.f. is given by
$$ \begin{aligned} f(x) &=\frac{1}{B(\alpha,\beta)}\cdot\frac{x^{\alpha-1}}{(1+x)^{\alpha+\beta}}; x>0, \alpha, \beta > 0. \end{aligned} $$
where,
-
$B(\alpha,\beta) =\frac{\Gamma \alpha \Gamma \beta}{\Gamma (\alpha+\beta)}=\int_0^1 x^{\alpha-1}(1-x)^{\beta-1}\; dx$is a beta function and -
$\Gamma \alpha$is a gamma function.
