# Inverse Beta distribution

This tool calculates the Inverse of Beta Cumulative Distribution Function. One of its uses is to calculate percentiles of a Beta distribution.

## Inverse Beta Distribution formulas

### Notations

X : a random variable following a beta distribution

`alpha` : shape parameter (> 0)

`beta` : second shape parameter (> 0)

The inverse of the cumulative distribution function F(x) is also called the 'quantile function', denoted Q(x). We have,

`F(x) = (Gamma(alpha+beta))/(Gamma(alpha)*Gamma(beta))*\int_-oo^xt^(alpha-1)(1-t)^(beta-1)\ dt`

`Q(x) = F^(-1)(x)`

For a probability p, quantile function Q gives a q value that verifies,

`q = Q(p) = F^(-1)(p)`

By definition of F, we have,

`P(X < q) = p`

`P(X < q)` is the pobability that X is less than q.

## See also

Gamma distribution Probabilities

Gamma distribution Chart

Statistics Calculators