<< distfun_nctrnd Noncentral T Distribution Noncentral Chi-Squared >>

distfun >> distfun > Noncentral T Distribution > distfun_nctstat

distfun_nctstat

Noncentral T mean and variance

Calling Sequence

M = distfun_nctstat ( v , delta )
[M,V] = distfun_nctstat ( v , delta )

Parameters

v :

a matrix of doubles, the number of degrees of freedom, v>0.

delta :

a matrix of doubles, the noncentrality parameter, delta is real

M :

a matrix of doubles, the mean

V :

a matrix of doubles, the variance

Description

Computes statistics from the Noncentral T distribution.

The mean of the Noncentral T distribution is

\begin{eqnarray}
M=\delta \sqrt{v/2} \frac{\Gamma((v-1)/2)}{\Gamma(v/2)}
\end{eqnarray}

if v > 1. M is undefined if 0 < v <= 1.

The variance of the Noncentral T distribution is

\begin{eqnarray}
V=\frac{v(1+\delta^2)}{v-2} - M^2
\end{eqnarray}

if v > 2. V is undefined if 0 < v <= 2.

Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.

Examples

delta=10;
v = [0.5 1 1.5 2 2.3 4];
[M,V]=distfun_nctstat(v,delta)
me=[%nan %nan %nan %nan 521.0145  44.920367]
ve=[%nan %nan 25.622878  17.724539  15.915993  12.533141]

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