naginterfaces.library.rand.dist_​expmix

naginterfaces.library.rand.dist_expmix(n, a, wgt, statecomm)

dist_expmix generates a vector of pseudorandom numbers from an exponential mix distribution composed of $m$ exponential distributions each having a mean $a_i$ and weight $w_i$.

For full information please refer to the NAG Library document for g05sg

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g05/g05sgf.html

Parameters

nint

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

afloat, array-like, shape $\left(\text{nmix}\right)$

The $m$ parameters $a_i$ for the $m$ exponential distributions in the mix.

wgtfloat, array-like, shape $\left(\text{nmix}\right)$

The $m$ weights $w_i$ for the $m$ exponential distributions in the mix.

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 exponential mix distribution.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $2$)

On entry, $\text{nmix}=⟨value⟩$.

Constraint: $\text{nmix}\ge 1$.

(errno $3$)

On entry, $a[⟨value⟩]=⟨value⟩$.

Constraint: $a[i-1]>0.0$.

(errno $4$)

On entry, $wgt[⟨value⟩]=⟨value⟩$.

Constraint: $wgt[i-1]\ge 0.0$.

(errno $4$)

On entry, sum of $wgt=⟨value⟩$.

Constraint: sum of $wgt=1.0$.

(errno $5$)

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

Notes

The distribution has PDF (probability density function)

$$\begin{array}{c}\begin{array}{cc}f\left(x\right)={\sum }_{i=1}^m\frac{1}{a_i}{w}_i{e}^{-x/a_i}& \text{if}x\ge 0\text{,}\\ f\left(x\right)=0& \text{otherwise,}\end{array}\end{array}$$

where ${\sum }_{i=1}^m{w}_i=1$ and $a_i>0$, $w_i\ge 0$.

dist_expmix returns the values $x_i$ by selecting, with probability $w_j$, random variates from an exponential distribution with parameter $a_j$.

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_expmix.

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