nctrnd

Noncentral t random numbers

Syntax

r = nctrnd(nu,delta)

r = nctrnd(nu,delta,sz1,...,szN)

r = nctrnd(nu,delta,sz)

Description

r = nctrnd(nu,delta) generates a random number drawn from a noncentral t distribution with nu degrees of freedom and the noncentrality parameter delta.

r = nctrnd(nu,delta,sz1,...,szN) generates an array of random numbers, where sz1,...,szN indicates the size of each dimension.

r = nctrnd(nu,delta,sz) generates an array of random numbers, where the vector sz specifies size(r).

Examples

Generate Random Numbers from Noncentral t Distribution

Generate 5000 random numbers from a noncentral t distribution with nu degrees of freedom and the noncentrality parameter delta.

rng(0,"twister") % For reproducibility
nu = 40;
delta = 4;
r = nctrnd(nu,delta,[5000 1]);

Plot a histogram of the numbers.

histogram(r)

Input Arguments

nu — Degrees of freedom

positive scalar | array of positive scalars

Degrees of freedom, specified as a positive scalar or an array of positive scalars.

To generate random numbers from multiple distributions, specify either nu or delta (or both) using arrays. If either nu or delta is an array, then the array sizes must be the same. In this case, nctrnd expands the scalar input into a constant array of the same size as the array input.

Data Types: single | double

delta — Noncentrality parameter

numeric scalar | numeric array

Noncentrality parameter, specified as a numeric scalar or array.

To generate random numbers from multiple distributions, specify either nu or delta (or both) using arrays. If either nu or delta is an array, then the array sizes must be the same. In this case, nctrnd expands the scalar input into a constant array of the same size as the array input.

Data Types: single | double

sz1,...,szN — Size of each dimension (as separate arguments)

integers

Size of each dimension, specified as separate arguments of integers. For example, specifying 5,3,2 generates a 5-by-3-by-2 array of random numbers from the probability distribution.

If either nu or delta is an array, then the specified dimensions sz1,...,szN must match the common dimensions of nu and delta after any necessary scalar expansion. The default values of sz1,...,szN are the common dimensions.

• If you specify a single value sz1, then r is a square matrix of size sz1-by-sz1.

• If the size of any dimension is 0 or negative, then r is an empty array.

• Beyond the second dimension, nctrnd ignores trailing dimensions with a size of 1. For example, specifying 3,1,1,1 produces a 3-by-1 vector of random numbers.

Data Types: single | double

sz — Size of each dimension (as a row vector)

row vector of integers

Size of each dimension, specified as a row vector of integers. For example, specifying [5,3,2] generates a 5-by-3-by-2 array of random numbers from the probability distribution.

If either nu or delta is an array, then the specified dimensions sz must match the common dimensions of nu and delta after any necessary scalar expansion. The default values of sz are the common dimensions.

• If you specify a single value [sz1], then r is a square matrix of size sz1-by-sz1.

• If the size of any dimension is 0 or negative, then r is an empty array.

• Beyond the second dimension, nctrnd ignores trailing dimensions with a size of 1. For example, specifying [3,1,1,1] produces a 3-by-1 vector of random numbers.

Data Types: single | double

Output Arguments

r — Random numbers

scalar value | array of scalar values

Random numbers, returned as a scalar value or an array of scalar values with the dimensions specified by sz1,...,szN or sz. Each element in r is the random number generated from the distribution specified by the corresponding elements in nu and delta.

Alternative Functionality

• nctrnd is a function specific to the noncentral t distribution. Statistics and Machine Learning Toolbox™ also offers the generic function random, which supports various probability distributions. To use random, specify the probability distribution name and its parameters. Note that the distribution-specific function nctrnd is faster than the generic function random.

• To generate random numbers interactively, use randtool, a user interface for random number generation.

References

[1] Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed., Hoboken, NJ: John Wiley & Sons, Inc., 1993, pp. 147–148.

[2] Johnson, N., and S. Kotz. Distributions in Statistics: Continuous Univariate Distributions-2. Hoboken, NJ: John Wiley & Sons, Inc., 1970, pp. 201–219.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The generated code can return a different sequence of numbers than MATLAB^® if either of the following is true:

• The output is nonscalar.

• An input parameter is invalid for the distribution.

For more information on code generation, see Introduction to Code Generation for Statistics and Machine Learning Functions and Overview of Code Generation Using MATLAB Coder (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