betainv

Beta inverse cumulative distribution function

Syntax

x = betainv(p,a,b)

Description

x = betainv(p,a,b) returns the inverse cumulative distribution function (icdf) of the beta distribution with the shape parameters a and b, evaluated at the probability values in p.

Examples

Inverse cdf of Beta Distribution

Compute the inverse cdf (icdf) values evaluated at the probability values in p for the beta distribution with the shape parameters a and b.

p = 0.005:0.01:0.995;
a = 10;
b = 5;
x = betainv(p,a,b);

Plot the icdf.

plot(p,x)
grid on
xlabel("p");
ylabel("x");

Input Arguments

p — Probability values at which to evaluate inverse of cdf

scalar value in the range [0,1] | array of scalar values in the range [0,1]

Probability values at which to evaluate the inverse of the cdf (icdf), specified as a scalar value or an array of scalar values in the range [0,1].

To evaluate the icdf at multiple values, specify p using an array. To evaluate the icdfs of multiple distributions, specify a and b using arrays. If one or more of the input arguments p, a, and b are arrays, then the array sizes must be the same. In this case, betainv expands each scalar input into a constant array of the same size as the array inputs. Each element in x is the icdf value of the distribution specified by the corresponding elements in a and b, evaluated at the corresponding element in p.

Data Types: single | double

a — First shape parameter

positive scalar value | array of positive scalar values

First shape parameter, specified as a positive scalar value or an array of positive scalar values.

To evaluate the icdf at multiple values, specify p using an array. To evaluate the icdfs of multiple distributions, specify a and b using arrays. If one or more of the input arguments p, a, and b are arrays, then the array sizes must be the same. In this case, betainv expands each scalar input into a constant array of the same size as the array inputs. Each element in x is the icdf value of the distribution specified by the corresponding elements in a and b, evaluated at the corresponding element in p.

Data Types: single | double

b — Second shape parameter

positive scalar value | array of positive scalar values

Second shape parameter, specified as a positive scalar value or an array of positive scalar values.

To evaluate the icdf at multiple values, specify p using an array. To evaluate the icdfs of multiple distributions, specify a and b using arrays. If one or more of the input arguments p, a, and b are arrays, then the array sizes must be the same. In this case, betainv expands each scalar input into a constant array of the same size as the array inputs. Each element in x is the icdf value of the distribution specified by the corresponding elements in a and b, evaluated at the corresponding element in p.

Data Types: single | double

Output Arguments

x — Inverse cdf values

scalar value | array of scalar values

Inverse cdf values evaluated at the probabilities in p, returned as a scalar value or an array of scalar values. x is the same size as p, a, and b after any necessary scalar expansion. Each element in x is the inverse cdf value of the distribution specified by the corresponding elements in a and b, evaluated at the corresponding probability in p.

More About

Beta Distribution

The inverse beta cdf for a given probability p and a given pair of parameters a and b is

$$x=F^{-1}(p|a,b)=\{x:F(x|a,b)=p\}$$

where

$$p=F(x|a,b)=\frac{1}{B(a,b)}{\displaystyle \underset{0}{\overset{x}{\int }}{t}^{a-1}{(1-t)}^{b-1}dt}$$

and B( · ) is the Beta function. Each element of x is the value whose cumulative probability under the beta cdf defined by the corresponding parameters in a and b is specified by the corresponding value in p.

For more information, see Beta Distribution.

Algorithms

The betainv function uses Newton's method with modifications to constrain steps to the allowable range for x [0,1].

Alternative Functionality

• betainv is a function specific to the beta distribution. Statistics and Machine Learning Toolbox™ also offers the generic function icdf, which supports various probability distributions. To use icdf, create a BetaDistribution probability distribution object and pass the object as an input argument or specify the probability distribution name and its parameters. Note that the distribution-specific function betainv is faster than the generic function icdf.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a