Generates a vector of random numbers from a triangular distribution, seeds and generator number passed explicitly

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NAG[g05lhc] NAG[nag_rngs_triangular] - Generates a vector of random numbers from a triangular distribution, seeds and generator number passed explicitly

Calling Sequence

g05lhc(xmin, xmax, xmed, n, x, igen, iseed, 'fail'=fail)

nag_rngs_triangular(. . .)

Parameters

xmin - float;
xmax - float;

On entry: the end points and of the uniform distribution.

Constraint: . .

xmed - float;

On entry: the median of the distribution (also the location of the vertex of the triangular distribution at which the PDF reaches a maximum).

Constraint: . .

n - integer;

On entry: , the number of pseudo-random numbers to be generated.

Constraint: . .

x - Vector(1..dim, datatype=float[8]);

Note: the dimension, dim, of the array x must be at least .

On exit: the pseudo-random numbers from the specified triangular distribution.

igen - integer;

On entry: must contain the identification number for the generator to be used to return a pseudo-random number and should remain unchanged following initialization by a prior call to one of the functions g05kbc (nag_rngs_init_repeatable) or g05kcc (nag_rngs_init_nonrepeatable).

iseed - Vector(1.., datatype=integer[kernelopts('wordsize')/8]);

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.

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_rngs_triangular (g05lhc) generates a vector of pseudo-random numbers from a triangular distribution with arguments , and .

Description

The triangular distribution has a PDF (probability density function) that is triangular in profile. The base of the triangle ranges from to and the PDF has a maximum value of at . If then with probability 1; otherwise the triangular distribution has PDF:

[[f(x)=(x-x[min])/(x[med]-x[min])*2/(x[max]-x[min]), x[min]<x<=x[med] ],[],[],[f(x)=(x[max]-x)/(x[max]-x[med])*2/(x[max]-x[min]), x[med]<x<=x[max] ],[],[],[f(x)=0, ]]

One of the initialization functions g05kbc (nag_rngs_init_repeatable) (for a repeatable sequence if computed sequentially) or g05kcc (nag_rngs_init_nonrepeatable) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_triangular (g05lhc).

	Error Indicators and Warnings
	"NE_BAD_PARAM" On entry, argument had an illegal value. "NE_INT" On entry, . Constraint: . "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 consult NAG for assistance. "NE_REAL_2" On entry, , . Constraint: . On entry, , . Constraint: . On entry, , . Constraint: .

	Accuracy
	Not applicable.

	Further Comments
	None.

Examples

>	xmin := -1: xmax := 1: xmed := 0.5: n := 5: igen := 1: x := Vector(5, datatype=float[8]): iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]): NAG:-g05lhc(xmin, xmax, xmed, n, x, igen, iseed):

iseed;

	See Also
	Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley g05 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.