Generates a vector of random numbers from an exponential mixture distribution, seeds and generator number passed explicitly

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NAG[g05lqc] NAG[nag_rngs_exp_mix] - Generates a vector of random numbers from an exponential mixture distribution, seeds and generator number passed explicitly

Calling Sequence

g05lqc(a, wgt, n, x, igen, iseed, 'nmix'=nmix, 'fail'=fail)

nag_rngs_exp_mix(. . .)

Parameters

a - Vector(1..nmix, datatype=float[8]);

On entry: the arguments for the exponential distributions in the mix.

Constraint: , for . .

wgt - Vector(1..nmix, datatype=float[8]);

On entry: the weights for the exponential distributions in the mix.

Constraints:

(∑)wgt[I]=1.0 ;

, for .

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 exponential mix 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.

'nmix'=nmix - integer; (optional)

On entry: , the number of exponential distributions in the mix.

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_rngs_exp_mix (g05lqc) generates a vector of pseudo-random numbers from an exponential mix distribution composed of exponential distributions each having a mean and weight .

Description

The distribution has PDF (probability density function)

$f(x)={[[(∑)1/(a[i])w[i]e^(-x/a[i]), x>0 ],[0, ]]$

where sum(w[i], i = 1 .. m) = 1 and , .

nag_rngs_exp_mix (g05lqc) returns the values by selecting, with probability , random variates from an exponential distribution with argument .

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_exp_mix (g05lqc).

Error Indicators and Warnings

"NE_ALLOC_FAIL"

Dynamic memory allocation failed.

"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"

On entry, sum of weights wgt is not equal to 1.0: sum .

"NE_REAL_ARRAY_ELEM_CONS"

On entry, : , .

	Accuracy
	Not applicable.

	Further Comments
	None.

Examples

nmix := 3:
n := 5:
igen := 1:
a := Vector([1, 5, 2], datatype=float[8]):
wgt := Vector([0.5, 0.3, 0.2], datatype=float[8]):
x := Vector(5, datatype=float[8]):
iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]):
NAG:-g05lqc(a, wgt, n, x, igen, iseed, 'nmix' = nmix):

wgt;

iseed;

	See Also
	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 g05 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.