# InverseBetaRegularized

InverseBetaRegularized[s,a,b]

gives the inverse of the regularized incomplete beta function.

# Examples

open allclose all

## Basic Examples(2)

Evaluate numerically:

Plot over a subset of the reals:

## Scope(17)

### Numerical Evaluation(4)

Evaluate numerically:

Evaluate to high precision:

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

Evaluate efficiently at high precision:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix InverseBetaRegularized function using MatrixFunction:

### 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:

### Function Properties(5)

is analytic on the open interval :

It has both singularities and discontinuities at the endpoints 0 or at 1:

is non-negative on the unit interval:

is injective:

is nondecreasing on the unit interval:

is neither convex nor concave on the unit interval:

### 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(2)

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

Compare binned modeled distribution with exact distribution:

A multivariate Student copula:

Probability density function:

## 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:

Wolfram Research (1996), InverseBetaRegularized, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseBetaRegularized.html.

#### Text

Wolfram Research (1996), InverseBetaRegularized, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseBetaRegularized.html.

#### CMS

Wolfram Language. 1996. "InverseBetaRegularized." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseBetaRegularized.html.

#### APA

Wolfram Language. (1996). InverseBetaRegularized. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseBetaRegularized.html

#### BibTeX

@misc{reference.wolfram_2024_inversebetaregularized, author="Wolfram Research", title="{InverseBetaRegularized}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/InverseBetaRegularized.html}", note=[Accessed: 17-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inversebetaregularized, organization={Wolfram Research}, title={InverseBetaRegularized}, year={1996}, url={https://reference.wolfram.com/language/ref/InverseBetaRegularized.html}, note=[Accessed: 17-September-2024 ]}