NAG Library Function Document

nag_rngs_lognormal (g05lkc)

+− Contents

1 Purpose

nag_rngs_lognormal (g05lkc) generates a vector of pseudorandom numbers from a log-normal distribution with parameters

μ

and

σ^{2}

#include <nag.h>

#include <nagg05.h>

void	nag_rngs_lognormal (double xmu, double var, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

The distribution has PDF (probability density function)

\begin{array}{l} f (x) = \frac{1}{x σ \sqrt{2 π}} \exp (- \frac{{(\ln x - μ)}^{2}}{2 σ^{2}}) & if ​ x > 0, \\ f (x) = 0 & otherwise, \end{array}

i.e.,

\ln x

is normally distributed with mean

μ

and variance

σ^{2}

. nag_rngs_lognormal (g05lkc) evaluates

\exp y_{i}

, where the

y_{i}

are generated by nag_rngs_normal (g05lac) from a Normal distribution with mean

μ

and variance

σ^{2}

One of the initialization functions nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_lognormal (g05lkc).

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

1: xmu – doubleInput: On entry: $μ$ , the mean of the distribution of $\ln x$ .
2: var – doubleInput: On entry: $σ^{2}$ , the variance of the distribution of $\ln x$ .
Constraint: $var \geq 0.0$ .
3: n – IntegerInput: On entry: $n$ , the number of pseudorandom numbers to be generated.
Constraint: $n \geq 0$ .
4: x[n] – doubleOutput: On exit: the $n$ pseudorandom numbers from the specified log-normal distribution.
5: igen – IntegerInput: On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
6: iseed[ $4$ ] – IntegerCommunication Array: On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
7: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_REAL: On entry, $var = 〈value〉$ .
Constraint: $var \geq 0.0$ .