## 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.