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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_copula_clayton (g05rh)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_rand_copula_clayton (g05rh) generates pseudorandom uniform variates with joint distribution of a Clayton/Cook–Johnson Archimedean copula.


[state, x, ifail] = g05rh(n, m, theta, sorder, state)
[state, x, ifail] = nag_rand_copula_clayton(n, m, theta, sorder, state)


Generates n pseudorandom uniform m-variates whose joint distribution is the Clayton/Cook–Johnson Archimedean copula Cθ, given by
Cθ = u1-θ + u2-θ + + um-θ - m + 1 -1/θ ,   θ 0, , uj 0,1 ,   j = 1 , m ;  
with the special case:
The generation method uses mixture of powers.
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 (g05rh).


Marshall A W and Olkin I (1988) Families of multivariate distributions Journal of the American Statistical Association 83 403
Nelsen R B (2006) An Introduction to Copulas (2nd Edition) Springer Series in Statistics


Compulsory Input Parameters

1:     n int64int32nag_int scalar
n, the number of pseudorandom uniform variates to generate.
Constraint: n0.
2:     m int64int32nag_int scalar
m, the number of dimensions.
Constraint: m2.
3:     theta – double scalar
θ, the copula parameter.
Constraint: theta1.0×10-6.
4:     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,,m.
Constraint: sorder=1 or 2.
5:     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


Output Parameters

1:     state: int64int32nag_int array
Contains updated information on the state of the generator.
2:     xldxsdx – double array
The pseudorandom uniform variates 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 of 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:
On entry, corrupt state argument.
Constraint: theta1.0×10-6.
Constraint: n0.
Constraint: m2.
On entry, invalid sorder.
Constraint: sorder=1 or 2.
On entry, ldx is too small: ldx=_.
On entry, sdx is too small: sdx=_.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


Not applicable.

Further Comments

In practice, the need for numerical stability restricts the range of θ such that:


This example generates thirteen four-dimensional variates for copula C1.3.
function g05rh_example

fprintf('g05rh 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
n = int64(13);
m = int64(4);
% Sample order
sorder = int64(1);

% Parameter
theta = 1.3;

% Generate variates
[state, x, ifail] = g05rh( ...
                           n, m, theta, sorder, state);

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

g05rh example results

Variates from a Clayton/Cook–Johnson copula
    0.8576    0.5048    0.9761    0.5895
    0.3186    0.6372    0.9959    0.5898
    0.9050    0.6950    0.9353    0.9329
    0.5278    0.1804    0.4177    0.2330
    0.1510    0.9777    0.2621    0.3867
    0.3906    0.7938    0.3073    0.3150
    0.1279    0.1709    0.1751    0.0568
    0.7613    0.4314    0.3498    0.2913
    0.3871    0.4430    0.3610    0.3774
    0.1242    0.0647    0.0472    0.0780
    0.6866    0.9500    0.9289    0.9763
    0.5259    0.8218    0.7134    0.4914
    0.0955    0.0459    0.1265    0.1947

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Chapter Contents
Chapter Introduction
NAG Toolbox

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