nag_rngs_triangular (g05lhc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rngs_triangular (g05lhc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_triangular (g05lhc) generates a vector of pseudorandom numbers from a triangular distribution with parameters xmin, xmax and xmed.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rngs_triangular (double xmin, double xmax, double xmed, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

The triangular distribution has a PDF (probability density function) that is triangular in profile. The base of the triangle ranges from x=xmin to x=xmax and the PDF has a maximum value of 2xmax-xmin  at x=xmed. If xmin=xmed=xmax then x=xmed with probability 1; otherwise the triangular distribution has PDF:
fx= x-xmin xmed-xmin ×2xmax-xmin ​ if ​xmin<xxmed, fx= xmax-x xmax-xmed ×2xmax-xmin ​ if ​xmed<xxmax, fx=0 ​ otherwise.
One of the initialization functions nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_triangular (g05lhc).

4  References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5  Arguments

1:     xmindoubleInput
2:     xmaxdoubleInput
On entry: the end points xmin and xmax of the uniform distribution.
Constraint: xminxmax.
3:     xmeddoubleInput
On entry: the median of the distribution xmed (also the location of the vertex of the triangular distribution at which the PDF reaches a maximum).
Constraint: xminxmedxmax.
4:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
5:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified triangular distribution.
6:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
7:     iseed[4]IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
8:     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, xmed=value and xmax=value.
Constraint: xmedxmax.
On entry, xmed=value and xmin=value.
Constraint: xmedxmin.
On entry, xmin=value and xmax=value.
Constraint: xminxmax.

7  Accuracy

Not applicable.

8  Further Comments


9  Example

This example prints five pseudorandom numbers from a triangular distribution with parameters xmin=-1.0, xmax=1.0 and xmed=0.5, generated by a single call to nag_rngs_triangular (g05lhc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05lhce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05lhce.r)

nag_rngs_triangular (g05lhc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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