g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rngs_f (g05ldc)

## 1  Purpose

nag_rngs_f (g05ldc) generates a vector of pseudorandom numbers taken from an $F$ (or Fisher's variance ratio) distribution with $\mu$ and $\nu$ degrees of freedom.

## 2  Specification

 #include #include
 void nag_rngs_f (Integer df1, Integer df2, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

## 3  Description

The distribution has PDF (probability density function)
 $fx= μ+ν-22 ! x12μ-1 12μ-1! 12ν-1! 1+μνx 12μ+ν × μν 12μ if ​x>0, fx=0 otherwise.$
nag_rngs_f (g05ldc) calculates the values
 $ν yi μ zi , i= 1,…,n,$
where ${y}_{i}$ and ${z}_{i}$ are generated by nag_rngs_gamma (g05lfc) from gamma distributions with parameters $\left(\frac{1}{2}\mu ,2\right)$ and $\left(\frac{1}{2}\nu ,2\right)$ respectively (i.e., from ${\chi }^{2}$-distributions with $\mu$ and $\nu$ degrees of freedom).
One of the initialization functions nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_f (g05ldc).

## 4  References

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

## 5  Arguments

1:     df1IntegerInput
On entry: $\mu$, the number of degrees of freedom of the distribution.
Constraint: ${\mathbf{df1}}\ge 1$.
2:     df2IntegerInput
On entry: $\nu$, the number of degrees of freedom of the distribution.
Constraint: ${\mathbf{df2}}\ge 1$.
3:     nIntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
4:     x[n]doubleOutput
On exit: the $n$ pseudorandom numbers from the specified $F$-distribution.
5:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
6:     iseed[$4$]IntegerCommunication Array
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.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{df1}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{df1}}\ge 1$.
On entry, ${\mathbf{df2}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{df2}}\ge 1$.
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
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 contact NAG for assistance.

## 7  Accuracy

Not applicable.

The time taken by nag_rngs_f (g05ldc) increases with $\mu$ and $\nu$.

## 9  Example

This example prints five pseudorandom numbers from an $F$-distribution with two and three degrees of freedom, generated by a single call to nag_rngs_f (g05ldc), after initialization by nag_rngs_init_repeatable (g05kbc).

### 9.1  Program Text

Program Text (g05ldce.c)

None.

### 9.3  Program Results

Program Results (g05ldce.r)