1: $x$ – double Input: On entry: the deviate from the noncentral $χ^{2}$ -distribution with $ν$ degrees of freedom and noncentrality parameter $λ$ .

Constraint: $x \geq 0.0$ .
2: $df$ – double Input: On entry: $ν$ , the degrees of freedom of the noncentral $χ^{2}$ -distribution.

Constraint: $df \geq 0.0$ .
3: $lambda$ – double Input: On entry: $λ$ , the noncentrality parameter of the noncentral $χ^{2}$ -distribution.

Constraint: $lambda \geq 0.0$ if $df > 0.0$ or $lambda > 0.0$ if $df = 0.0$ .
4: $tol$ – double Input: On entry: the required accuracy of the solution. If g01gcc is entered with tol greater than or equal to $1.0$ or less than $10 \times machine precision$ (see X02AJC), the value of $10 \times machine precision$ is used instead.
5: $max_iter$ – Integer Input: On entry: the maximum number of iterations to be performed.

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

Constraint: $max_iter \geq 1$ .
6: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_2_REAL_ARG_CONS: On entry, $df = 0.0$ and $lambda = 0.0$ .
Constraint: $lambda > 0.0$ if $df = 0.0$ .
NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_CHI_PROB: The calculations for the central chi-square probability has failed to converge. A larger value of tol should be used.
NE_CONV: The solution has failed to converge in $〈value〉$ iterations. Consider increasing max_iter or tol.
NE_INT_ARG_LT: On entry, $max_iter = 〈value〉$ .
Constraint: $max_iter \geq 1$ .
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 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_POISSON_WEIGHT: 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.
NE_REAL_ARG_LT: On entry, $df = 〈value〉$ .
Constraint: $df \geq 0.0$ .

On entry, $lambda = 〈value〉$ .
Constraint: $lambda \geq 0.0$ .

On entry, $x = 〈value〉$ .
Constraint: $x \geq 0.0$ .
NE_TERM_LARGE: 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 lambda are too large.

7 Accuracy

The summations described in Section 3 are made until an upper bound on the truncation error relative to the current summation value is less than tol.

8 Parallelism and Performance

g01gcc is not threaded in any implementation.

9 Further Comments

The number of terms in (1) required for a given accuracy will depend on the following factors:

(i)The rate at which the Poisson weights tend to zero. This will be slower for larger values of $λ$ .
(ii)The rate at which the central $χ^{2}$ probabilities tend to zero. This will be slower for larger values of $ν$ and $x$ .