nag_rand_bivariate_copula_clayton (g05rec) (PDF version)
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g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_bivariate_copula_clayton (g05rec)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_bivariate_copula_clayton (g05rec) generates pseudorandom uniform bivariates with joint distribution of a Clayton/Cook–Johnson Archimedean copula.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_bivariate_copula_clayton (Nag_OrderType order, Integer state[], double theta, Integer n, double x[], Integer pdx, Integer sdx, NagError *fail)

3  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_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_bivariate_copula_clayton (g05rec).

4  References

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

5  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     state[dim]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
3:     thetadoubleInput
On entry: θ, the copula parameter.
Constraint: theta-1.0.
4:     nIntegerInput
On entry: n, the number of bivariates to generate.
Constraint: n0.
5:     x[pdx×sdx]doubleOutput
Note: where Xi,j appears in this document, it refers to the array element x[j-1×pdx+i-1].
On exit: the n bivariate uniforms with joint distribution described by Cθ, with Xi,j holding the ith value for the jth dimension if order=Nag_ColMajor and the jth value for the ith dimension of order=Nag_RowMajor.
6:     pdxIntegerInput
On entry: the stride separating matrix row elements in the array x.
Constraints:
  • if order=Nag_ColMajor, pdxn;
  • if order=Nag_RowMajor, pdx2.
7:     sdxIntegerInput
On entry: the secondary dimension of X.
Constraints:
  • if order=Nag_ColMajor, sdx2;
  • if order=Nag_RowMajor, sdxn.
8:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pdx must be at least value: pdx=value.
On entry, sdx must be at least value: sdx=value.
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.
NE_INVALID_STATE
On entry, corrupt state argument.
NE_REAL
On entry, invalid theta: theta=value.
Constraint: theta-1.0.

7  Accuracy

Not applicable.

8  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_real_safe_small_number (X02AMC); and ε is the machine precision returned by nag_machine_precision (X02AJC).

9  Example

This example generates thirteen variates for copula C-0.8.

9.1  Program Text

Program Text (g05rece.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05rece.r)


nag_rand_bivariate_copula_clayton (g05rec) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012