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NAG Toolbox: nag_rand_dist_chisq (g05sd)

Purpose

nag_rand_dist_chisq (g05sd) generates a vector of pseudorandom numbers taken from a χ2χ2-distribution with νν degrees of freedom.

Syntax

[state, x, ifail] = g05sd(n, df, state)
[state, x, ifail] = nag_rand_dist_chisq(n, df, state)

Description

The distribution has PDF (probability density function)
f(x) = ( xν / 21 × ex / 2 )/( 2ν / 2 × (ν / 21) ! ) if ​ x > 0 ;
f(x) = 0 otherwise.
f(x) = x ν/2-1 × e -x/2 2 ν/2 × ( ν/2-1 ) ! if ​ x>0 ; f(x)=0 otherwise.
This is the same as a gamma distribution with parameters ν / 2ν/2 and 22.
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_chisq (g05sd).

References

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

Parameters

Compulsory Input Parameters

1:     n – int64int32nag_int scalar
nn, the number of pseudorandom numbers to be generated.
Constraint: n0n0.
2:     df – int64int32nag_int scalar
νν, the number of degrees of freedom of the distribution.
Constraint: df1 df1 .
3:     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 χ2χ2-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, df < 1df<1.
  ifail = 3ifail=3
On entry,state vector was not initialized or has been corrupted.

Accuracy

Not applicable.

Further Comments

The time taken by nag_rand_dist_chisq (g05sd) increases with νν.

Example

function nag_rand_dist_chisq_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
df = int64(5);
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_chisq(n, df, state)
 

state =

                   17
                 1234
                    1
                    0
                 3990
                  775
                 3088
                31015
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    4.4731
    5.9371
    1.7636
    2.9812
    4.3280


ifail =

                    0


function g05sd_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
df = int64(5);
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05sd(n, df, state)
 

state =

                   17
                 1234
                    1
                    0
                 3990
                  775
                 3088
                31015
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    4.4731
    5.9371
    1.7636
    2.9812
    4.3280


ifail =

                    0



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Chapter Introduction
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