NAG CL Interface
g05skc (dist_​normal)

1 Purpose

g05skc generates a vector of pseudorandom numbers taken from a Normal (Gaussian) distribution with mean μ and variance σ2.

2 Specification

#include <nag.h>
void  g05skc (Integer n, double xmu, double var, Integer state[], double x[], NagError *fail)
The function may be called by the names: g05skc, nag_rand_dist_normal or nag_rand_normal.

3 Description

The distribution has PDF (probability distribution function)
fx=1σ2π exp- x-μ 22σ2 .  
g05skc uses the algorithm of Wichura (1988).
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 g05skc.

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
Wichura (1988) Algorithm AS 241: the percentage points of the Normal distribution Appl. Statist. 37 477–484

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.
3: var double Input
On entry: σ2, the variance of the distribution.
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 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.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g05skc 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 Normal distribution with mean 1.0 and variance 1.5, generated by a single call to g05skc, after initialization by g05kfc.

10.1 Program Text

Program Text (g05skce.c)

10.2 Program Data


10.3 Program Results

Program Results (g05skce.r)