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distfun >> distfun > Noncentral F Distribution > distfun_ncfstat

distfun_ncfstat

Noncentral F mean and variance

Calling Sequence

M = distfun_ncfstat(v1,v2,delta)
[M,V] = distfun_ncfstat(v1,v2,delta)

Parameters

v1 :

a matrix of doubles, numerator degrees of freedom, v1>0 (can be non integer).

v2 :

a matrix of doubles, denominator degrees of freedom, v2>0 (can be non integer).

delta :

a matrix of doubles, the noncentrality parameter, delta>=0

M :

a matrix of doubles, the mean

V :

a matrix of doubles, the variance

Description

Computes statistics from the Noncentral F-distribution.

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

The mean of the Noncentral F distribution is

\begin{eqnarray}
M &=& \frac{v_2(v_1+\delta)}{v_1(v_2-2)}
\end{eqnarray}

if v2>2, and M is set to %nan otherwise.

The variance of the Noncentral F distribution is

\begin{eqnarray}
V &=& 2 \frac{(v_1+\delta)^2+(v_1+2\delta)(v_2-2)}{(v_2-2)^2(v_2-4)} \left(\frac{v_2}{v_1}\right)^2
\end{eqnarray}

if v2>4, and V is set to %nan otherwise.

Examples

// Test with scalar v1 and v2
[M,V] = distfun_ncfstat(4,12,0.3)
Me = 1.29
Ve = 1.451025

Bibliography

http://en.wikipedia.org/wiki/Noncentral_F-distribution

Authors


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