LevyFlightDistribution Class Reference

Levy Flight distribution. More...

#include <ql/experimental/math/levyflightdistribution.hpp>

Public Member Functions
Constructors
	LevyFlightDistribution (Real xm=1.0, Real alpha=1.0)
	LevyFlightDistribution (const param_type &parm)
	Constructs a LevyFlightDistribution from its parameters.

Inspectors
Real	xm () const
	Returns the xm parameter of the distribution.
Real	alpha () const
	Returns the alpha parameter of the distribution.
Real min	BOOST_PREVENT_MACRO_SUBSTITUTION () const
	Returns the smallest value that the distribution can produce.
Real max	BOOST_PREVENT_MACRO_SUBSTITUTION () const
	Returns the largest value that the distribution can produce.
param_type	param () const
	Returns the parameters of the distribution.
void	param (const param_type &parm)
	Sets the parameters of the distribution.
void	reset ()
Real	operator() (Real x) const
	Returns the value of the pdf for x.
template<class Engine>
Real	operator() (Engine &eng) const
template<class Engine>
Real	operator() (Engine &eng, const param_type &parm) const

Detailed Description

Levy Flight distribution.

The levy flight distribution is a random distribution with the following form:

\[p(x) = \frac{\alpha x_m^{\alpha}}{x^{\alpha+1}} \]

with support over \( x \in [x_m, \infty) \) and the parameter \( \alpha > 0 \).

Levy Flight is normally defined as \( x_m = 1 \) and \( 0 < \alpha < 2 \), which is where \( p(x) \) has an infinite variance. However, the more general version, known as Pareto Type I, is well defined for \( \alpha > 2 \), so the current implementation does not restrict \( \alpha \) to be smaller than 2.

Constructor & Destructor Documentation

LevyFlightDistribution()

LevyFlightDistribution ( Real xm = 1.0, Real alpha = 1.0 )

explicit

Constructs a LevyFlightDistribution with a given xm and alpha Requires: alpha > 0

Member Function Documentation

reset()

void reset

(

)

Effects: Subsequent uses of the distribution do not depend on values produced by any engine prior to invoking reset.

operator()() [1/2]

template<class Engine>

Real operator()

(

Engine &

eng

)

const

Returns a random variate distributed according to the levy flight distribution.

operator()() [2/2]

template<class Engine>

Real operator()	(	Engine &	eng,
		const param_type &	parm ) const

Returns a random variate distributed according to the levy flight with parameters specified by parm