For very large values of both and , greater than , a normal approximation is used. If only one of or is greater than then a approximation is used; see Abramowitz and Stegun (1972).
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth
1: – Real (Kind=nag_wp)Input
On entry: , the lower tail probability from the required -distribution.
2: – Real (Kind=nag_wp)Input
On entry: the degrees of freedom of the numerator variance, .
3: – Real (Kind=nag_wp)Input
On entry: the degrees of freedom of the denominator variance, .
4: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended since useful values can be provided in some output arguments even when on exit. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
Note: in some cases g01fdf may return useful information.
If on exit , or , then g01fdf returns .
On entry, .
On entry, .
On entry, and .
Constraint: and .
The solution has failed to converge. However, the result should be a reasonable approximation. Alternatively, g01fef can be used with a suitable setting of the argument tol.
The probability is too close to or . The value of cannot be computed. This will only occur when the large sample approximations are used.
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
The result should be accurate to five significant digits.
8Parallelism and Performance
g01fdf is not threaded in any implementation.
For higher accuracy g01fef can be used along with the transformations given in Section 3.
This example reads the lower tail probabilities for several -distributions, and calculates and prints the corresponding deviates until the end of data is reached.