nag_rand_lognormal (g05smc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
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

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n0.
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_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_REAL
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

None.

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

None.

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