naginterfaces.library.rand.dist_​exp

naginterfaces.library.rand.dist_exp(n, a, statecomm)

dist_exp generates a vector of pseudorandom numbers from a (negative) exponential distribution with mean $a$.

For full information please refer to the NAG Library document for g05sf

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g05/g05sff.html

Parameters

nint

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

afloat

$a$, the mean 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 exponential distribution.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $2$)

On entry, $a=⟨value⟩$.

Constraint: $a>0.0$.

(errno $3$)

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

Notes

The exponential distribution has PDF (probability density function):

$$\begin{array}{c}\begin{array}{cc}f\left(x\right)=\frac{1}{a}{e}^{-x/a}& \text{if}x\ge 0\text{,}\\ & \\ f\left(x\right)=0& \text{otherwise.}\end{array}\end{array}$$

dist_exp returns the values

$$x_i=-aln\left(y_i\right)$$

where $y_i$ are the next $n$ numbers generated by a uniform $(0,1]$ generator.

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_exp.

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