NAG C Library Function Document

nag_rand_bivariate_copula_clayton (g05rec)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{order}$ – Nag_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 $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2:    $\mathbf{state}\left[\mathit{dim}\right]$ – IntegerCommunication Array

Note: the dimension, $\mathit{dim}$, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to 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:    $\mathbf{theta}$ – doubleInput

On entry: $\theta$, the copula parameter.

Constraint: $\mathbf{theta}\ge -1.0$.

4:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of bivariates to generate.

Constraint: $\mathbf{n}\ge 0$.

5:    $\mathbf{x}\left[\mathbf{pdx}\times \mathbf{sdx}\right]$ – doubleOutput

Note: where $\mathbf{X}\left(i,j\right)$ appears in this document, it refers to the array element $\mathbf{x}\left[\left(j-1\right)\times \mathbf{pdx}+i-1\right]$.

On exit: the $n$ bivariate uniforms with joint distribution described by $C_{\theta }$, with $\mathbf{X}\left(i,j\right)$ holding the $i$th value for the $j$th dimension if $\mathbf{order}=\mathrm{Nag\_ColMajor}$ and the $j$th value for the $i$th dimension if $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

6:    $\mathbf{pdx}$ – IntegerInput

On entry: the stride separating matrix row elements in the array x.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdx}\ge \mathbf{n}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdx}\ge 2$.

7:    $\mathbf{sdx}$ – IntegerInput

On entry: the secondary dimension of X.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{sdx}\ge 2$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{sdx}\ge \mathbf{n}$.

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

NE_INT_2

On entry, pdx must be at least $〈\mathit{\text{value}}〉$: $\mathbf{pdx}=〈\mathit{\text{value}}〉$.

On entry, sdx must be at least $〈\mathit{\text{value}}〉$: $\mathbf{sdx}=〈\mathit{\text{value}}〉$.

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_INVALID_STATE

On entry, corrupt state argument.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL

On entry, invalid theta: $\mathbf{theta}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{theta}\ge -1.0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g05rece.c)

10.2

Program Data

10.3

Program Results

Program Results (g05rece.r)