betaincinv

Beta inverse cumulative distribution function

Syntax

x = betaincinv(y,z,w)
x = betaincinv(y,z,w,tail)


Description

x = betaincinv(y,z,w) computes the inverse incomplete beta function for corresponding elements of y, z, and w, such that y = betainc(x,z,w). The elements of y must be in the closed interval [0,1], and those of z and w must be nonnegative. y, z, and w must all be real and the same size (or any of them can be scalar).

x = betaincinv(y,z,w,tail) specifies the tail of the incomplete beta function. Choices are 'lower' (the default) to use the integral from 0 to x, or 'upper' to use the integral from x to 1. These two choices are related as follows: betaincinv(y,z,w,'upper') = betaincinv(1-y,z,w,'lower'). When y is close to 0, the 'upper' option provides a way to compute x more accurately than by subtracting y from 1.

More About

Inverse Incomplete Beta Function

The incomplete beta function is defined as $$x=I^{-1}(y,z,w)$$, such that

$$y=I(x,z,w)=\frac{1}{\beta (z,w)}{\displaystyle \underset{0}{\overset{x}{\int }}{t}^{(z-1)}{(1-t)}^{(w-1)}dt}$$

betaincinv computes the inverse of the incomplete beta function with respect to the integration limit x using Newton's method.

Extended Capabilities

Tall Arrays

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

The betaincinv 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 betaincinv 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 in R2009a