betainc

Incomplete beta function

Syntax

I = betainc(X,Z,W) I = betainc(X,Z,W,tail)

Description

I = betainc(X,Z,W) computes the incomplete beta function for corresponding elements of the arrays X, Z, and W. The elements of X must be in the closed interval [0,1]. The arrays Z and W must be nonnegative and real. All arrays must be the same size, or any of them can be scalar.

I = betainc(X,Z,W,tail) specifies the tail of the incomplete beta function. Choices are:

`'lower'` (the default)	Computes the integral from `0` to `x`
`'upper'`	Computes the integral from `x` to `1`

These functions are related as follows:

1-betainc(X,Z,W) = betainc(X,Z,W,'upper')

Note that especially when the upper tail value is close to 0, it is more accurate to use the 'upper' option than to subtract the 'lower' value from 1.

Examples

collapse all

Compute Incomplete Beta Function

Open Live Script

Compute the incomplete beta function corresponding to the elements of Z according to the parameters X and W.

format longG
X = 0.5;
Z = (1:10)';
W = 3;
I = betainc(X,Z,W)

I = 10×1

                     0.875
                    0.6875
                       0.5
                   0.34375
                 0.2265625
                0.14453125
                0.08984375
                 0.0546875
             0.03271484375
            0.019287109375

More About

collapse all

Incomplete Beta Function

The incomplete beta function is

$I_{x} (z, w) = \frac{1}{B (z, w)} \int_{0}^{x} t^{z - 1} {(1 - t)}^{w - 1} d t$

where $B (z, w)$ , the beta function, is defined as

$B (z, w) = \int_{0}^{1} t^{z - 1} {(1 - t)}^{w - 1} d t = \frac{Γ (z) Γ (w)}{Γ (z + w)}$

and $Γ (z)$ is the gamma function.

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

The betainc function fully supports tall arrays. For more information, see Tall Arrays.

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

Usage notes and limitations:

Always returns a complex result.
Strict single-precision calculations are not supported. In the generated code, single-precision inputs produce single-precision outputs. However, variables inside the function might be double-precision.

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

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

The betainc function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a