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NAG Toolbox: nag_rand_dist_triangular (g05sp)

Purpose

nag_rand_dist_triangular (g05sp) generates a vector of pseudorandom numbers from a triangular distribution with parameters xminxmin, xmedxmed and xmaxxmax.

Syntax

[state, x, ifail] = g05sp(n, xmin, xmed, xmax, state)
[state, x, ifail] = nag_rand_dist_triangular(n, xmin, xmed, xmax, state)

Description

The triangular distribution has a PDF (probability density function) that is triangular in profile. The base of the triangle ranges from x = xminx=xmin to x = xmaxx=xmax and the PDF has a maximum value of 2/(xmaxxmin) 2xmax-xmin  at x = xmedx=xmed. If xmin = xmed = xmaxxmin=xmed=xmax then x = xmedx=xmed with probability 1; otherwise the triangular distribution has PDF:
f(x) = (xxmin)/(xmedxmin) × 2/(xmaxxmin) ​ if ​xminxxmed,
f(x) = (xmaxx)/(xmaxxmed) × 2/(xmaxxmin) ​ if ​xmed < xxmax,
f(x) = 0 ​ otherwise.
f(x) = x-xmin xmed-xmin × 2 xmax-xmin ​ if ​xminxxmed, f(x)= xmax-x xmax-xmed ×2xmax-xmin ​ if ​xmed<xxmax, f(x)=0 ​ otherwise.
One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_dist_triangular (g05sp).

References

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

Parameters

Compulsory Input Parameters

1:     n – int64int32nag_int scalar
nn, the number of pseudorandom numbers to be generated.
Constraint: n0n0.
2:     xmin – double scalar
The end point xminxmin of the triangular distribution.
3:     xmed – double scalar
The median of the distribution xmedxmed (also the location of the vertex of the triangular distribution at which the PDF reaches a maximum).
Constraint: xmedxminxmedxmin.
4:     xmax – double scalar
The end point xmaxxmax of the triangular distribution.
Constraint: xmaxxmedxmaxxmed.
5:     state( : :) – int64int32nag_int array
Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).
Contains information on the selected base generator and its current state.

Optional Input Parameters

None.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

1:     state( : :) – int64int32nag_int array
Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).
Contains updated information on the state of the generator.
2:     x(n) – double array
The nn pseudorandom numbers from the specified triangular distribution.
3:     ifail – int64int32nag_int scalar
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry, n < 0n<0.
  ifail = 3ifail=3
On entry, xmed < xminxmed<xmin.
  ifail = 4ifail=4
On entry, xmax < xmedxmax<xmed.
  ifail = 5ifail=5
On entry,state vector was not initialized or has been corrupted.

Accuracy

Not applicable.

Further Comments

None.

Example

function nag_rand_dist_triangular_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
xmin = -1;
xmed = 0.5;
xmax = 1;
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_triangular(n, xmin, xmed, xmax, state)
 

state =

                   17
                 1234
                    1
                    0
                 4110
                11820
                23399
                29340
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    0.3817
   -0.4348
    0.4960
    0.5509
   -0.4398


ifail =

                    0


function g05sp_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
xmin = -1;
xmed = 0.5;
xmax = 1;
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05sp(n, xmin, xmed, xmax, state)
 

state =

                   17
                 1234
                    1
                    0
                 4110
                11820
                23399
                29340
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    0.3817
   -0.4348
    0.4960
    0.5509
   -0.4398


ifail =

                    0



PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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