tstat

Student's t mean and variance

Syntax

[m,v] = tstat(nu)

Description

[m,v] = tstat(nu) returns the mean and variance of the Student's t distribution with nu degrees of freedom.

Examples

Compute Mean and Variance of Student's t Distribution

Compute the mean and variance for Student's t distribution with degrees of freedom nu equal to 1 to 30.

nu = reshape(1:30,6,5);
[m,v] = tstat(nu)

m = 6×5

   NaN     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0

v = 6×5

       NaN    1.4000    1.1818    1.1176    1.0870
       NaN    1.3333    1.1667    1.1111    1.0833
    3.0000    1.2857    1.1538    1.1053    1.0800
    2.0000    1.2500    1.1429    1.1000    1.0769
    1.6667    1.2222    1.1333    1.0952    1.0741
    1.5000    1.2000    1.1250    1.0909    1.0714

Note that the mean is undefined for 1 degree of freedom, and variance is undefined for 1 and 2 degrees of freedom.

Input Arguments

nu — Degrees of freedom

positive scalar value | array of positive scalar values

Degrees of freedom for the Student's t distribution, specified as a positive scalar value or an array of positive scalar values.

Example: [9,19,49,99]

Data Types: single | double

Output Arguments

m — Mean

scalar value | array of scalar values

Mean of the Student's t distribution with the degrees of freedom specified in nu, returned as a scalar value or an array of scalar values. m is the same size as nu.

v — Variance

scalar value | array of scalar values

Variance of the Student's t distribution with the degrees of freedom specified in nu, returned as a scalar value or an array of scalar values. v is the same size as nu.

More About

Mean and Variance of Student’s t Distribution

The parameters of the Student's t distribution depend on the degrees of freedom.

The mean of the Student’s t distribution is μ = 0 for degrees of freedom ν greater than 1. If ν equals 1, then the mean is undefined.

The variance of the Student’s t distribution is $$\frac{\nu }{\nu -2}$$ for degrees of freedom ν greater than 2. If ν is less than or equal to 2, then the variance is undefined.

For more information, see Student's t Distribution.

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).