The routine may be called by the names g01muf or nagf_stat_pdf_vavilov.
g01muf evaluates an approximation to the Vavilov density function given by
where and ,
is an arbitrary real constant and
is the exponential integral, and is Euler's constant.
The method used is based on Fourier expansions. Further details can be found in
For values of , the Vavilov distribution can be replaced by the Landau distribution since . For values of , the Vavilov distribution can be replaced by a Gaussian distribution with mean and variance .
Schorr B (1974) Programs for the Landau and the Vavilov distributions and the corresponding random numbers Comp. Phys. Comm.7 215–224
1: – Real (Kind=nag_wp)Input
On entry: the argument of the function.
2: – Real (Kind=nag_wp) arrayCommunication Array
On entry: this must be the same argument rcomm as returned by a previous call to g01zuf.
3: – 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. 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:
Either the initialization routine has not been called prior to the first call of this routine or a communication array has become corrupted.
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.
At least five significant digits are usually correct.
8Parallelism and Performance
g01muf is not threaded in any implementation.
g01muf can be called repeatedly with different values of provided that the values of and remain unchanged between calls. Otherwise, g01zuf must be called again. This is illustrated in Section 10.
This example evaluates at ,
and , and prints the results.