nag_rand_lognormal (g05smc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rand_lognormal (g05smc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_lognormal (g05smc) generates a vector of pseudorandom numbers from a log-normal distribution with parameters μ and σ2.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_lognormal (Integer n, double xmu, double var, Integer state[], double x[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx = 1 xσ2π exp - lnx-μ 2 2σ2 if ​ x>0 , fx=0 otherwise,
i.e., lnx is normally distributed with mean μ and variance σ2. nag_rand_lognormal (g05smc) evaluates expyi, where the yi are generated by nag_rand_normal (g05skc) with mean μ and variance σ2, for i=1,2,,n.
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_lognormal (g05smc).

4  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

5  Arguments

1:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     xmudoubleInput
On entry: μ, the mean of the distribution of lnx.
3:     vardoubleInput
On entry: σ2, the variance of the distribution of lnx.
Constraint: var0.0.
4:     state[dim]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
5:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified log-normal distribution.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n0.
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.
On entry, state vector has been corrupted or not initialized.
On entry, var=value.
Constraint: var0.0.
On entry, xmu is too large to take the exponential of xmu=value.

7  Accuracy

Not applicable.

8  Further Comments


9  Example

This example prints five pseudorandom numbers from a log-normal distribution with mean 1.0 and variance 2.0, generated by a single call to nag_rand_lognormal (g05smc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05smce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05smce.r)

nag_rand_lognormal (g05smc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012