NAG CL Interface
g01muc (pdf_​vavilov)

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1 Purpose

g01muc returns the value of the Vavilov density function ϕV(λ;κ,β2).
It is intended to be used after a call to g01zuc.

2 Specification

#include <nag.h>
double  g01muc (double x, const double comm_arr[])
The function may be called by the names: g01muc, nag_stat_pdf_vavilov or nag_prob_density_vavilov.

3 Description

g01muc evaluates an approximation to the Vavilov density function ϕV(λ;κ,β2) given by
ϕV(λ;κ,β2)=12πi c-i c+ieλsf(s;κ,β2)ds,  
where κ>0 and 0β21, c is an arbitrary real constant and
f(s;κ,β2)=C(κ,β2)exp{slnκ+(s+κβ2)[ln(sκ)+E1(sκ)]-κexp(-sκ)} .  
E1(x)=0xt-1(1-e-t)dt is the exponential integral, C(κ,β2)=exp{κ(1+γβ2)} and γ is Euler's constant.
The method used is based on Fourier expansions. Further details can be found in Schorr (1974).
For values of κ0.01, the Vavilov distribution can be replaced by the Landau distribution since λV=(λL-lnκ)/κ. For values of κ10, the Vavilov distribution can be replaced by a Gaussian distribution with mean μ=γ-1-β2-lnκ and variance σ2=(2-β2)/2κ.

4 References

Schorr B (1974) Programs for the Landau and the Vavilov distributions and the corresponding random numbers Comp. Phys. Comm. 7 215–224

5 Arguments

1: x double Input
On entry: the argument λ of the function.
2: comm_arr[322] const double Communication Array
On entry: this must be the same argument comm_arr as returned by a previous call to g01zuc.

6 Error Indicators and Warnings


7 Accuracy

At least five significant digits are usually correct.

8 Parallelism and Performance

g01muc is not threaded in any implementation.

9 Further Comments

g01muc can be called repeatedly with different values of λ provided that the values of κ and β2 remain unchanged between calls. Otherwise, g01zuc must be called again. This is illustrated in Section 10.

10 Example

This example evaluates ϕV(λ;κ,β2) at λ=2.5, κ=0.4 and β2=0.1, and prints the results.

10.1 Program Text

Program Text (g01muce.c)

10.2 Program Data

Program Data (g01muce.d)

10.3 Program Results

Program Results (g01muce.r)