NAG C Library Function Document

nag_prob_non_central_chi_sq (g01gcc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{x}$ – doubleInput

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:    $\mathbf{df}$ – doubleInput

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

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

3:    $\mathbf{lambda}$ – doubleInput

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

Constraint: $\mathbf{lambda}\ge 0.0$ if $\mathbf{df}>0.0$ or $\mathbf{lambda}>0.0$ if $\mathbf{df}=0.0$.

4:    $\mathbf{tol}$ – doubleInput

On entry: the required accuracy of the solution. If nag_prob_non_central_chi_sq (g01gcc) is entered with tol greater than or equal to $1.0$ or less than $10\times \mathit{machine precision}$ (see nag_machine_precision (X02AJC)), the value of $10\times \mathit{machine precision}$ is used instead.

5:    $\mathbf{max\_iter}$ – IntegerInput

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

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

Constraint: $\mathbf{max\_iter}\ge 1$.

6:    $\mathbf{fail}$ – 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_2_REAL_ARG_CONS

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

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_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 $〈\mathit{\text{value}}〉$ iterations. Consider increasing max_iter or tol.

NE_INT_ARG_LT

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

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

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_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, $\mathbf{df}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df}\ge 0.0$.

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

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

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

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01gcce.c)

10.2

Program Data

Program Data (g01gcce.d)

10.3

Program Results

Program Results (g01gcce.r)