naginterfaces.library.rand.dist_​weibull

naginterfaces.library.rand.dist_weibull(n, a, b, statecomm)

dist_weibull generates a vector of pseudorandom numbers from a two parameter Weibull distribution with shape parameter $a$ and scale parameter $b$.

For full information please refer to the NAG Library document for g05ss

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g05/g05ssf.html

Parameters

nint

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

afloat

$a$, the shape parameter of the distribution.

bfloat

$b$, the scale parameter 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 Weibull 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, $b=⟨value⟩$.

Constraint: $b>0.0$.

(errno $4$)

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

Notes

The distribution has PDF (probability density function)

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

dist_weibull returns the value ${(-bln\left(y\right))}^{1/a}$, where $y$ is a pseudorandom number from a uniform distribution over $(0,1]$.

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_weibull.

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