naginterfaces.library.rand.dist_​logistic

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

dist_logistic generates a vector of pseudorandom numbers from a logistic distribution with mean $a$ and spread $b$.

For full information please refer to the NAG Library document for g05sl

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g05/g05slf.html

Parameters

nint

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

afloat

$a$, the mean of the distribution.

bfloat

$b$, the spread of the distribution, where ‘spread’ is $\frac{\sqrt{3}}{\pi }\times$standard deviation.

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 logistic distribution.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $3$)

On entry, $b=⟨value⟩$.

Constraint: $b\ge 0.0$.

(errno $4$)

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

Notes

The distribution has PDF (probability density function)

$$f\left(x\right)=\frac{e^{(x-a)/b}}{b{(1+e^{(x-a)/b})}^2}\text{.}$$

dist_logistic returns the value

$$a+bln\left(\frac{y}{1-y}\right)\text{,}$$

where $y$ is a pseudorandom number uniformly distributed 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_logistic.

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