NAG Library Function Document

nag_prob_non_central_f_dist (g01gdc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     f – doubleInput

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

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

2:     df1 – doubleInput

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

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

3:     df2 – doubleInput

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

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

4:     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:     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)), then the value of $10\times \mathit{machine precision}$ is used instead.

6:     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:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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.

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  Further Comments

9  Example

9.1  Program Text

Program Text (g01gdce.c)

9.2  Program Data

Program Data (g01gdce.d)

9.3  Program Results

Program Results (g01gdce.r)