NAG Library Routine Document

g01gcf  (prob_chisq_noncentral)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{x}$ – 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:     $\mathbf{df}$ – 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:     $\mathbf{rlamda}$ – 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:     $\mathbf{tol}$ – 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), the value of $10\times \mathit{machine precision}$ is used instead.

5:     $\mathbf{maxit}$ – IntegerInput

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

Suggested value: $100$. See Section 9 for further discussion.

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

6:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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 arguments 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, $\mathbf{df}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df}\ge 0.0$.

On entry, $\mathbf{df}=0.0$ and $\mathbf{rlamda}=0.0$.
Constraint: $\mathbf{rlamda}>0.0$ if $\mathbf{df}=0.0$.

On entry, $\mathbf{maxit}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{maxit}\ge 1$.

On entry, $\mathbf{rlamda}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{rlamda}\ge 0.0$.

On entry, $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\ge 0.0$.

$\mathbf{ifail}=2$

The initial value of the Poisson weight used in the summation of (1) (see Section 3) was too small to be calculated. The computed probability is likely to be zero.

$\mathbf{ifail}=3$

The solution has failed to converge in $〈\mathit{\text{value}}〉$ iterations. Consider increasing maxit or tol.

$\mathbf{ifail}=4$

The value of a term required in (2) (see Section 3) is too large to be evaluated accurately. The most likely cause of this error is both x and rlamda are too large.

$\mathbf{ifail}=5$

The calculations for the central chi-square probability has failed to converge. A larger value of tol should be used.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01gcfe.f90)

10.2

Program Data

Program Data (g01gcfe.d)

10.3

Program Results

Program Results (g01gcfe.r)