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NAG Toolbox: nag_rand_copula_clayton_bivar (g05re)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_rand_copula_clayton_bivar (g05re) generates pseudorandom uniform bivariates with joint distribution of a Clayton/Cook–Johnson Archimedean copula.

Syntax

[state, x, ifail] = g05re(n, theta, sorder, state)
[state, x, ifail] = nag_rand_copula_clayton_bivar(n, theta, sorder, state)

Description

Generates pseudorandom uniform bivariates u1,u20,12 whose joint distribution is the Clayton/Cook–Johnson Archimedean copula Cθ with parameter θ, given by
Cθ = max u1 -θ + u2 -θ -1 ,0 -1/θ ,   θ -1, 0  
with the special cases:
The generation method uses conditional sampling.
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_copula_clayton_bivar (g05re).

References

Nelsen R B (2006) An Introduction to Copulas (2nd Edition) Springer Series in Statistics

Parameters

Compulsory Input Parameters

1:     n int64int32nag_int scalar
n, the number of bivariates to generate.
Constraint: n0.
2:     theta – double scalar
θ, the copula parameter.
Constraint: theta-1.0.
3:     sorder int64int32nag_int scalar
Determines the storage order of variates; the i,jth variate is stored in xij if sorder=1, and xji if sorder=2, for i=1,2,,n and j=1,2.
Constraint: sorder=1 or 2.
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.

Output Parameters

1:     state: int64int32nag_int array
Contains updated information on the state of the generator.
2:     xldxsdx – double array
The n bivariate uniforms with joint distribution described by Cθ, with xij holding the ith value for the jth dimension if sorder=1 and the jth value for the ith dimension if sorder=2.
3:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
   ifail=1
On entry, corrupt state argument.
   ifail=2
Constraint: theta-1.0.
   ifail=3
Constraint: n0.
   ifail=4
On entry, invalid sorder.
Constraint: sorder=1 or 2.
   ifail=6
On entry, ldx is too small: ldx=_.
   ifail=7
On entry, sdx is too small: sdx=_.
   ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
   ifail=-399
Your licence key may have expired or may not have been installed correctly.
   ifail=-999
Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

In practice, the need for numerical stability restricts the range of θ such that: where εs is the safe-range parameter, the value of which is returned by nag_machine_real_safe (x02am); and ε is the machine precision returned by nag_machine_precision (x02aj).

Example

This example generates thirteen variates for copula C-0.8.
function g05re_example


fprintf('g05re example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(1762543)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% Sample size and order
n      = int64(13);
sorder = int64(1);

% Parameter
theta = -0.8;

% Generate variates
[state, x, ifail] = g05re( ...
                           n, theta, sorder, state);

disp('Variates from bivariate Clayton/Cook–Johnson copula');
disp(x);


g05re example results

Variates from bivariate Clayton/Cook–Johnson copula
    0.6400    0.2223
    0.1154    0.8101
    0.7486    0.1439
    0.8003    0.1062
    0.1135    0.9946
    0.4975    0.7655
    0.3904    0.4925
    0.7892    0.1196
    0.5032    0.4116
    0.6750    0.2093
    0.0600    0.9055
    0.2655    0.7085
    0.6276    0.2370


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