Lévy Flight

New in version 0.5.

This function generates Levy flight by integration of Levy alpha-stable distribution (also reffered just as stable distribution).

The Levy distribution is defined by two parameters \(\alpha\) and \(\beta\). The Gaussian distribution is special case of Levy distribution with \(\alpha=2\) and \(\beta=0\). In case of Gaussian distribution the Levy flight is Brownian walk.

This function uses Lévy Noise (Skewed Stable Random Variable Generator).

Example Usage

The following example produce 500 samples of Levy flight produced from Levy noise located (mean value) at 0 (position), with characteristic exponent index of 1.8 (alpha), skeewness of 0 (beta) and diffusion of 1. (sigma).

import signalz
x = signalz.levy_flight(500, alpha=1.8, beta=0., sigma=1., position=0)

Function Documentation

signalz.generators.levy_flight.levy_flight(n, alpha=2.0, beta=1.0, sigma=1.0, position=0.0)[source]

This function produces Levy flight.

Args:

  • n - length of the output data (int) - how many samples will be on output

Kwargs:

  • alpha - characteristic exponent index of used Levy noise (float) in range 0<alpha<2
  • beta - skeewness of used Levy noise (float) in range -1<beta<1
  • sigma - diffusion of used Levy noise (float), in case of gaussian distribution it is standard deviation
  • position - position parameter (float) of used Levy noise

Returns:

  • vector of values representing the flight (1d array)