nag_rand_lognormal (g05smc) (PDF version)
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NAG Library Manual

NAG Library Function Document

nag_rand_lognormal (g05smc)


    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:     n IntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     xmu doubleInput
On entry: μ, the mean of the distribution of lnx.
3:     var doubleInput
On entry: σ2, the variance of the distribution of lnx.
Constraint: var0.0.
4:     state[dim] IntegerCommunication Array
Note: the dimension, dim, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to 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:     fail NagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
See Section in the Essential Introduction for further information.
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.
An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.
On entry, state vector has been corrupted or not initialized.
Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.
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  Parallelism and Performance

nag_rand_lognormal (g05smc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9  Further Comments


10  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).

10.1  Program Text

Program Text (g05smce.c)

10.2  Program Data


10.3  Program Results

Program Results (g05smce.r)

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

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015