NAG Library Routine Document

G01GCF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     X – REAL (KIND=nag_wp)Input

On entry: the deviate from the noncentral ${\chi }^2$-distribution with $\nu$ degrees of freedom and noncentrality parameter $\lambda$.

Constraint: $\mathbf{X}\ge 0.0$.

2:     DF – REAL (KIND=nag_wp)Input

On entry: $\nu$, the degrees of freedom of the noncentral ${\chi }^2$-distribution.

Constraint: $\mathbf{DF}\ge 0.0$.

3:     RLAMDA – REAL (KIND=nag_wp)Input

On entry: $\lambda$, the noncentrality parameter of the noncentral ${\chi }^2$-distribution.

Constraint: $\mathbf{RLAMDA}\ge 0.0$ if $\mathbf{DF}>0.0$ or $\mathbf{RLAMDA}>0.0$ if $\mathbf{DF}=0.0$.

4:     TOL – REAL (KIND=nag_wp)Input

On entry: the required accuracy of the solution. If G01GCF is entered with TOL greater than or equal to $1.0$ or less than $10\times \mathit{machine precision}$ (see X02AJF), then the value of $10\times \mathit{machine precision}$ is used instead.

5:     MAXIT – INTEGERInput

On entry: the maximum number of iterations to be performed.

Suggested value: $100$. See Section 8 for further discussion.

Constraint: $\mathbf{MAXIT}\ge 1$.

6:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, because for this routine the values of the output parameters may be useful even if $\mathbf{IFAIL}\ne \mathbf{0}$ on exit, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	$\mathbf{DF}<0.0$,
or	$\mathbf{RLAMDA}<0.0$,
or	$\mathbf{DF}=0.0$ and $\mathbf{RLAMDA}=0.0$,
or	$\mathbf{X}<0.0$,
or	$\mathbf{MAXIT}<1$.

$\mathbf{IFAIL}=2$

The initial value of the Poisson weight used in the summation (1) was too small to be calculated. The value of $P\left(\mathbf{X}\le x:\nu \text{;}\lambda \right)$ is likely to be zero.

$\mathbf{IFAIL}=3$

The solution has failed to converge in MAXIT iterations.

$\mathbf{IFAIL}=4$

The value of a term required in (2) is too large to be evaluated accurately. The most likely cause of this error is both X and RLAMDA being very large.

$\mathbf{IFAIL}=5$

The calculations for the central ${\chi }^2$ probability has failed to converge. This is an unlikely error exit. A larger value of TOL should be used.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01gcfe.f90)

9.2  Program Data

Program Data (g01gcfe.d)

9.3  Program Results

Program Results (g01gcfe.r)