# tstat

Student's t mean and variance

## Description

example

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

## Examples

collapse all

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

collapse all

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

collapse all

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.

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.

collapse all

### 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.