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NAG Toolbox: nag_rand_dist_f (g05sh)

Purpose

nag_rand_dist_f (g05sh) generates a vector of pseudorandom numbers taken from an FF (or Fisher's variance ratio) distribution with μμ and νν degrees of freedom.

Syntax

[state, x, ifail] = g05sh(n, df1, df2, state)
[state, x, ifail] = nag_rand_dist_f(n, df1, df2, state)

Description

The distribution has PDF (probability density function)
f (x) = ( (( μ + ν2 )/2) ! x (1/2) μ1 )/( ((1/2)μ1) ! ((1/2)ν1) ! (1 + μ/νx) (1/2) (μ + ν) ) × (μ/ν)(1/2)μ if ​ x > 0 ,
f(x) = 0 otherwise.
f (x) = ( μ+ν-2 2 ) ! x 12 μ-1 ( 12 μ-1)! (12 ν-1 ) ! ( 1+ μν x ) 12 (μ+ν) × (μν) 12μ if ​ x>0 , f(x)=0 otherwise.
nag_rand_dist_f (g05sh) calculates the values
(ν yi)/(μ zi) ,   i = 1,2,,n ,
ν yi μ zi ,   i=1,2,,n ,
where yiyi and zizi are generated by nag_rand_dist_gamma (g05sj) from gamma distributions with parameters ((1/2)μ,2)(12μ,2) and ((1/2)ν,2)(12ν,2) respectively (i.e., from χ2χ2-distributions with μμ and νν degrees of freedom).
One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_dist_f (g05sh).

References

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

Parameters

Compulsory Input Parameters

1:     n – int64int32nag_int scalar
nn, the number of pseudorandom numbers to be generated.
Constraint: n0n0.
2:     df1 – int64int32nag_int scalar
μμ, the number of degrees of freedom of the distribution.
Constraint: df11df11.
3:     df2 – int64int32nag_int scalar
νν, the number of degrees of freedom of the distribution.
Constraint: df21df21.
4:     state( : :) – int64int32nag_int array
Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).
Contains information on the selected base generator and its current state.

Optional Input Parameters

None.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

1:     state( : :) – int64int32nag_int array
Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).
Contains updated information on the state of the generator.
2:     x(n) – double array
The nn pseudorandom numbers from the specified FF-distribution.
3:     ifail – int64int32nag_int scalar
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry, n < 0n<0.
  ifail = 2ifail=2
On entry, df1 < 1df1<1.
  ifail = 3ifail=3
On entry, df2 < 1df2<1.
  ifail = 4ifail=4
On entry,state vector was not initialized or has been corrupted.

Accuracy

Not applicable.

Further Comments

The time taken by nag_rand_dist_f (g05sh) increases with μμ and νν.

Example

function nag_rand_dist_f_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
df1 = int64(2);
df2 = int64(3);
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_f(n, df1, df2, state)
 

state =

                   17
                 1234
                    1
                    0
                18942
                20099
                15825
                20302
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    1.4401
    1.8083
    0.3638
    0.5464
    4.0895


ifail =

                    0


function g05sh_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
df1 = int64(2);
df2 = int64(3);
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05sh(n, df1, df2, state)
 

state =

                   17
                 1234
                    1
                    0
                18942
                20099
                15825
                20302
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    1.4401
    1.8083
    0.3638
    0.5464
    4.0895


ifail =

                    0



PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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