NAG FL Interface
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: $\mathbf{maxit}$ – Integer Input

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: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $-1$ is recommended since useful values can be provided in some output arguments even when $\mathbf{ifail}\ne \mathbf{0}$ on exit. When the value $-\mathbf{1}$ or $\mathbf{1}$ 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 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results