NAG CL Interface
g05smc (dist_​lognormal)

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1 Purpose

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

2 Specification

#include <nag.h>
void  g05smc (Integer n, double xmu, double var, Integer state[], double x[], NagError *fail)
The function may be called by the names: g05smc, nag_rand_dist_lognormal or nag_rand_lognormal.

3 Description

The distribution has PDF (probability density function)
f(x) = 1 xσ2π exp(- (lnx-μ) 2 2σ2 ) if ​ x>0 , f(x)=0 otherwise,  
i.e., lnx is normally distributed with mean μ and variance σ2. g05smc evaluates expyi, where the yi are generated by g05skc with mean μ and variance σ2, for i=1,2,,n.
One of the initialization functions g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to 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 Integer Input
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2: xmu double Input
On entry: μ, the mean of the distribution of lnx.
3: var double Input
On entry: σ2, the variance of the distribution of lnx.
Constraint: var0.0.
4: state[dim] Integer Communication 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] double Output
On exit: the n pseudorandom numbers from the specified log-normal distribution.
6: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface 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.
See Section 7.5 in the Introduction to the NAG Library CL Interface 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 8 in the Introduction to the NAG Library CL Interface 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

Background information to multithreading can be found in the Multithreading documentation.
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 g05smc, after initialization by g05kfc.

10.1 Program Text

Program Text (g05smce.c)

10.2 Program Data


10.3 Program Results

Program Results (g05smce.r)