LevyFlightDistribution Class Reference

Levy Flight distribution as needed by Boost Random. More...

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

## Public Types

typedef Real | input_type
typedef Real | result_type

## 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 >
result_type | operator() (Engine &eng) const
template<class Engine >
result_type | operator() (Engine &eng, const param_type &parm) const
| BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR (os, LevyFlightDistribution, ed)
| Writes the distribution to a std::ostream.
| BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR (is, LevyFlightDistribution, ed)
| Reads the distribution from a std::istream.
| BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR (LevyFlightDistribution, lhs, rhs)

## Detailed Description

Levy Flight distribution as needed by Boost Random.

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]

result_type operator() | ( | Engine & | eng | ) | const

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

## operator()() [2/2]

result_type operator() | ( | Engine & | eng,
|  | const param_type & | parm
| ) |  | const

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

## BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR()

BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR | ( | LevyFlightDistribution | ,
|  | lhs | ,
|  | rhs |
| ) |  |

Returns true iff the two distributions will produce identical sequences of values given equal generators.