NAG Library Function Document
nag_prob_density_vavilov (g01muc) returns the value of the Vavilov density function .
It is intended to be used after a call to nag_init_vavilov (g01zuc)
||nag_prob_density_vavilov (double x,
const double comm_arr)
nag_prob_density_vavilov (g01muc) evaluates an approximation to the Vavilov density function
is an arbitrary real constant and
is the exponential integral,
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
x – doubleInput
On entry: the argument of the function.
comm_arr – const doubleCommunication Array
: this must
be the same argument comm_arr
as returned by a previous call to nag_init_vavilov (g01zuc)
6 Error Indicators and Warnings
At least five significant digits are usually correct.
nag_prob_density_vavilov (g01muc) can be called repeatedly with different values of
provided that the values of
remain unchanged between calls. Otherwise, nag_init_vavilov (g01zuc)
must be called again. This is illustrated in Section 9
This example evaluates at , and , and prints the results.
9.1 Program Text
Program Text (g01muce.c)
9.2 Program Data
Program Data (g01muce.d)
9.3 Program Results
Program Results (g01muce.r)