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NAG[g05lfc] NAG[nag_rngs_gamma] - Generates a vector of random numbers from a  distribution, seeds and generator number passed explicitly
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Calling Sequence
g05lfc(a, b, n, x, igen, iseed, 'fail'=fail)
nag_rngs_gamma(. . .)
Parameters
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a - float;
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On entry:  , the argument of the gamma distribution.
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Constraint:  . .
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b - float;
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On entry:  , the argument of the gamma distribution.
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Constraint:  . .
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n - integer;
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On entry:  , the number of pseudo-random numbers to be generated.
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Constraint:  . .
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x - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array x must be at least  .
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On exit: the  pseudo-random numbers from the specified gamma distribution.
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iseed - Vector(1.. , datatype=integer[kernelopts('wordsize')/8]);
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On entry: contains values which define the current state of the selected generator.
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On exit: contains updated values defining the new state of the selected generator.
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_rngs_gamma (g05lfc) generates a vector of pseudo-random numbers taken from a gamma distribution with  and  .
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Description
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The gamma distribution has PDF (probability density function)
![[[f(x)=1/(b^aGAMMA(a))x^(a-1)e^(-x/b), 0<=x a,b>0.0],[],[f(x)=0, ]]](/support/helpjp/helpview.aspx?si=9893/file08498/math130.png)
One of three algorithms is used to generate the variates depending upon the value of  :
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if  , the gamma distribution reduces to the exponential distribution and the method based on the logarithmic transformation of a uniform random variate is used;
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if  , the algorithm given by Best (1978) is used. This is based on using a Student's  -distribution with two degrees of freedom as the target distribution in an envelope rejection method.
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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_gamma (g05lfc).
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Error Indicators and Warnings
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"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,  . Constraint:  .
On entry,  . Constraint:  .
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Examples
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a := 5:
b := 1:
n := 5:
igen := 1:
x := Vector(5, datatype=float[8]):
iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]):
NAG:-g05lfc(a, b, n, x, igen, iseed):
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See Also
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Ahrens J H and Dieter U (1974) Computer methods for sampling from gamma, beta, Poisson and binomial distributions Computing 12 223–46
Best D J (1978) Letter to the Editor Appl. Statist. 27 181
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworths
g05 Chapter Introduction.
NAG Toolbox Overview.
NAG Web Site.
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