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NAG[g05ldc] NAG[nag_rngs_f] - Generates a vector of random numbers from an  -distribution, seeds and generator number passed explicitly
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Calling Sequence
g05ldc(df1, df2, n, x, igen, iseed, 'fail'=fail)
nag_rngs_f(. . .)
Parameters
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df1 - integer;
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On entry:  , the number of degrees of freedom of the distribution.
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Constraint:  . .
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df2 - integer;
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On entry:  , the number of degrees of freedom of the 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  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_f (g05ldc) generates a vector of pseudo-random numbers taken from a  (or Fisher's variance ratio) distribution with  and  degrees of freedom.
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Description
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The distribution has PDF (probability density function)
![[[f(x)=(((mu+nu-2)/2)!x^(1/2mu-1))/((1/2,mu,-,1)!(1/2,nu,-,1)!(1,+,mu/nu,x)^(1/2(mu,+,nu)))*(mu/nu)^(1/2mu), x>0 ],[,],[f(x)=0, ]]](/support/helpjp/helpview.aspx?si=9892/file08496/math134.png)
nag_rngs_f (g05ldc) calculates the values
![nu*y[i]*i/(mu*z[i]) = 1, () .. (), n](/support/helpjp/helpview.aspx?si=9892/file08496/math138.png)
where ![y[i]](/support/helpjp/helpview.aspx?si=9892/file08496/math141.png) and ![z[i]](/support/helpjp/helpview.aspx?si=9892/file08496/math143.png) are generated by g05lfc (nag_rngs_gamma) from gamma distributions with arguments  and  respectively (i.e., from  -distributions with  and  degrees of freedom).
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_f (g05ldc).
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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:  .
On entry,  . Constraint:  .
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.
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Further Comments
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The time taken by nag_rngs_f (g05ldc) increases with  and  .
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Examples
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>
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df1 := 2:
df2 := 3:
n := 5:
igen := 1:
x := Vector(5, datatype=float[8]):
iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]):
NAG:-g05ldc(df1, df2, n, x, igen, iseed):
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