# InverseBetaRegularized

InverseBetaRegularized[s,a,b]

gives the inverse of the regularized incomplete beta function.

# Details # Examples

open allclose all

## Basic Examples(2)

Evaluate numerically:

Plot over a subset of the reals:

## Scope(11)

### Numerical Evaluation(3)

Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

### Specific Values(4)

Values of InverseBetaRegularized at fixed points:

Values at zero:

Find a value of z for which the InverseBetaRegularized[z,1,2]=0.5:

### Visualization(2)

Plot the InverseBetaRegularized function for different values of parameter a:

Plot the InverseBetaRegularized function for different values of parameter b:

### Differentiation(2)

First derivative with respect to s when a=2 and b=3:

First derivative with respect to a when b=2:

First derivative with respect to b when a=2:

Higher derivatives with respect to s when a=2 and b=3:

Plot the higher derivatives with respect to s when a=2 and b=3:

## Generalizations & Extensions(2)

Evaluate the 4-argument generalized case:

## Applications(1)

Model the PDF of the beta distribution through uniformly distributed random numbers:

Compare binned modeled distribution with exact distribution:

## Properties & Relations(2)

InverseBetaRegularized is the inverse of BetaRegularized:

Solve a transcendental equation: ## Possible Issues(2)

InverseBetaRegularized evaluates numerically only for :

In TraditionalForm, is not automatically interpreted as an inverse regularized beta function: