## 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.