nag_rand_triangular (g05spc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_triangular (g05spc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_triangular (g05spc) generates a vector of pseudorandom numbers from a triangular distribution with parameters xmin, xmed and xmax.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_triangular (Integer n, double xmin, double xmed, double xmax, Integer state[], double x[], 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 × 2 xmax-xmin ​ if ​xminxxmed, fx= xmax-x xmax-xmed ×2xmax-xmin ​ if ​xmed<xxmax, fx=0 ​ otherwise.
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_triangular (g05spc).

4  References

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:     xmindoubleInput
On entry: the end point xmin of the triangular distribution.
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: xmedxmin.
4:     xmaxdoubleInput
On entry: the end point xmax of the triangular distribution.
Constraint: xmaxxmed.
5:     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.
6:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified triangular distribution.
7:     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_2
On entry, xmax=value and xmed=value.
Constraint: xmaxxmed.
On entry, xmed=value and xmin=value.
Constraint: xmedxmin.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

This example prints five pseudorandom numbers from a triangular distribution with parameters xmin=-1.0, xmed=0.5 and xmax=1.0, generated by a single call to nag_rand_triangular (g05spc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05spce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05spce.r)


nag_rand_triangular (g05spc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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