naginterfaces.library.rand.dist_​lognormal

naginterfaces.library.rand.dist_lognormal(n, xmu, var, statecomm)

dist_lognormal generates a vector of pseudorandom numbers from a log-normal distribution with parameters $\mu$ and ${\sigma }^2$.

For full information please refer to the NAG Library document for g05sm

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g05/g05smf.html

Parameters

nint

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

xmufloat

$\mu$, the mean of the distribution of $ln\left(x\right)$.

varfloat

${\sigma }^2$, the variance of the distribution of $ln\left(x\right)$.

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 log-normal distribution.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $2$)

On entry, $xmu$ is too large to take the exponential of $xmu=⟨value⟩$.

(errno $3$)

On entry, $var=⟨value⟩$.

Constraint: $var\ge 0.0$.

(errno $4$)

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

Notes

The distribution has PDF (probability density function)

$$\begin{array}{c}\begin{array}{cc}f\left(x\right)=\frac{1}{x\sigma \sqrt{2\pi }}exp(-\frac{{(ln\left(x\right)-\mu )}^2}{2{\sigma }^2})& \text{if}x>0\text{,}\\ & \\ f\left(x\right)=0& \text{otherwise,}\end{array}\end{array}$$

i.e., $ln\left(x\right)$ is normally distributed with mean $\mu$ and variance ${\sigma }^2$. dist_lognormal evaluates $exp\left(y_i\right)$, where the $y_i$ are generated by dist_normal() from a Normal distribution with mean $\mu$ and variance ${\sigma }^2$, for $\text{i}=1,2,\dots ,n$.

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_lognormal.

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