NAG Library Function Document

nag_prob_non_central_f_dist (g01gdc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{f}$ – doubleInput

On entry: $f$, the deviate from the noncentral $F$-distribution.

Constraint: $\mathbf{f}>0.0$.

2:    $\mathbf{df1}$ – doubleInput

On entry: the degrees of freedom of the numerator variance, ${\nu }_1$.

Constraint: $0.0<\mathbf{df1}\le {10}^6$.

3:    $\mathbf{df2}$ – doubleInput

On entry: the degrees of freedom of the denominator variance, ${\nu }_2$.

Constraint: $\mathbf{df2}>0.0$.

4:    $\mathbf{lambda}$ – doubleInput

On entry: $\lambda$, the noncentrality parameter.

Constraint: $0.0\le \mathbf{lambda}\le -2.0\log \left(U\right)$ where $U$ is the safe range parameter as defined by nag_real_safe_small_number (X02AMC).

5:    $\mathbf{tol}$ – doubleInput

On entry: the relative accuracy required by you in the results. If nag_prob_non_central_f_dist (g01gdc) 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.

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

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

Suggested value: $500$. See nag_prob_non_central_chi_sq (g01gcc) and nag_prob_non_central_beta_dist (g01gec) for further details.

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

7:    $\mathbf{fail}$ – 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_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_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_PROB_F

The required probability cannot be computed accurately. This may happen if the result would be very close to zero or one. Alternatively the values of df1 and f may be too large. In the latter case you could try using a normal approximation, see Abramowitz and Stegun (1972).

NE_PROB_F_INIT

The required accuracy was not achieved when calculating the initial value of the central $F$ or ${\chi }^2$ probability. You should try a larger value of tol. If the ${\chi }^2$ approximation is being used then nag_prob_non_central_f_dist (g01gdc) returns zero otherwise the value returned should be an approximation to the correct value.

NE_REAL_ARG_CONS

On entry, $\mathbf{df1}=〈\mathit{\text{value}}〉$.
Constraint: $0.0<\mathbf{df1}\le {10}^6$.

On entry, $\mathbf{df1}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df1}>0.0$.

On entry, $\mathbf{lambda}=〈\mathit{\text{value}}〉$.
Constraint: $0.0\le \mathbf{lambda}\le -2.0\times \log \left(U\right)$, where $U$ is the safe range parameter as defined by nag_real_safe_small_number (X02AMC).

NE_REAL_ARG_LE

On entry, $\mathbf{df2}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df2}>0.0$.

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

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01gdce.c)

10.2

Program Data

Program Data (g01gdce.d)

10.3

Program Results

Program Results (g01gdce.r)