InverseBetaRegularized

InverseBetaRegularized[s,a,b]

gives the inverse of the regularized incomplete beta function.

Details

Examples

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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:

TraditionalForm formatting:

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)

TemplateBox[{x, 3, 2}, InverseBetaRegularized] is analytic on the open interval :

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

TemplateBox[{x, 3, 2}, InverseBetaRegularized] is non-negative on the unit interval:

TemplateBox[{x, 3, 2}, InverseBetaRegularized] is injective:

TemplateBox[{x, 3, 2}, InverseBetaRegularized] is nondecreasing on the unit interval:

TemplateBox[{x, 3, 2}, InverseBetaRegularized] 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)

InverseBetaRegularized threads elementwise over lists:

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_2025_inversebetaregularized, author="Wolfram Research", title="{InverseBetaRegularized}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/InverseBetaRegularized.html}", note=[Accessed: 25-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_inversebetaregularized, organization={Wolfram Research}, title={InverseBetaRegularized}, year={1996}, url={https://reference.wolfram.com/language/ref/InverseBetaRegularized.html}, note=[Accessed: 25-May-2025 ]}