Class describing the Vavilov pdf.
The probability density function of the Vavilov distribution
is given by:
\f[ p(\lambda; \kappa, \beta^2) =
\frac{1}{2 \pi i}\int_{c-i\infty}^{c+i\infty} \phi(s) e^{\lambda s} ds\f]
where \f$\phi(s) = e^{C} e^{\psi(s)}\f$
with \f$ C = \kappa (1+\beta^2 \gamma )\f$
and \f$\psi(s)&=& s \ln \kappa + (s+\beta^2 \kappa)
\cdot \left ( \int \limits_{0}^{1}
\frac{1 - e^{\frac{-st}{\kappa}}}{t} \,\der t- \gamma \right )
- \kappa \, e^{\frac{-s}{\kappa}}\f$.
\f$ \gamma = 0.5772156649\dots\f$ is Euler's constant.
The parameters are:
- 0: Norm: Normalization constant
- 1: x0: Location parameter
- 2: xi: Width parameter
- 3: kappa: Parameter \f$\kappa\f$ of the Vavilov distribution
- 4: beta2: Parameter \f$\beta^2\f$ of the Vavilov distribution
Benno List, June 2010
@ingroup StatFunc