# nctstat

Noncentral t mean and variance

## Syntax

```[M,V] = nctstat(NU,DELTA) ```

## Description

`[M,V] = nctstat(NU,DELTA)` returns the mean of and variance for the noncentral t pdf with `NU` degrees of freedom and noncentrality parameter `DELTA`. `NU` and `DELTA` can be vectors, matrices, or multidimensional arrays that all have the same size, which is also the size of `M` and `V`. A scalar input for `NU` or `DELTA` is expanded to a constant array with the same dimensions as the other input.

The mean of the noncentral t distribution with parameters ν and δ is

`$\frac{\delta {\left(\nu /2\right)}^{1/2}\Gamma \left(\left(\nu -1\right)/2\right)}{\Gamma \left(\nu /2\right)}$`

where ν > 1.

The variance is

`$\frac{\nu }{\left(\nu -2\right)}\left(1+{\delta }^{2}\right)-\frac{\nu }{2}{\delta }^{2}{\left[\frac{\Gamma \left(\left(\nu -1\right)/2\right)}{\Gamma \left(\nu /2\right)}\right]}^{2}$`

where ν > 2.

## Examples

```[m,v] = nctstat(10,1) m = 1.0837 v = 1.3255```

## References

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

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