# Inverse Student's t-distribution

This tool calculates the Inverse of Student's Cumulative Distribution Function.

## Inverse Student's t-Distribution formulas

X : a random variable following a exponential distribution of parameter `k > 0` (degrees of freedom).

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

`F(x) = 1/2+x*Gamma((k+1)/2)* (\text{}_2F_1(1/2,(k+1)/2;3/2;-x^2/k))/(sqrt(k*pi)*Gamma(k/2))`

where `\text{}_2F_1` is the hypergeometric function.

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

## See also

Student's t-distribution Probabilities

Student's t-distribution Chart

Statistics Calculators