naginterfaces.library.rand.dist_​chisq

naginterfaces.library.rand.dist_chisq(n, df, statecomm)

dist_chisq generates a vector of pseudorandom numbers taken from a ${\chi }^2$-distribution with $\nu$ degrees of freedom.

For full information please refer to the NAG Library document for g05sd

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g05/g05sdf.html

Parameters

nint

$n$, the number of pseudorandom numbers to be generated.

dfint

$\nu$, the number of degrees of freedom of the distribution.

statecommdict, RNG communication object, modified in place

RNG communication structure.

This argument must have been initialized by a prior call to init_repeat() or init_nonrepeat().

Returns

xfloat, ndarray, shape $\left(n\right)$

The $n$ pseudorandom numbers from the specified ${\chi }^2$-distribution.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $2$)

On entry, $df=⟨value⟩$.

Constraint: $df\ge 1$.

(errno $3$)

On entry, $statecomm$[‘state’] vector has been corrupted or not initialized.

Notes

The distribution has PDF (probability density function)

$$\begin{array}{c}\begin{array}{cc}f\left(x\right)=\frac{x^{\nu /2-1}\times e^{-x/2}}{2^{\nu /2}\times (\nu /2-1)!}& \text{if}x>0\text{;}\\ & \\ f\left(x\right)=0& \text{otherwise.}\end{array}\end{array}$$

This is the same as a gamma distribution with parameters $\nu /2$ and $2$.

One of the initialization functions init_repeat() (for a repeatable sequence if computed sequentially) or init_nonrepeat() (for a non-repeatable sequence) must be called prior to the first call to dist_chisq.

References

Kendall, M G and Stuart, A, 1969, The Advanced Theory of Statistics (Volume 1), (3rd Edition), Griffin

Knuth, D E, 1981, The Art of Computer Programming (Volume 2), (2nd Edition), Addison–Wesley