Lévy Walk¶

New in version 0.5.

This function generates Levy walk by interpolation of Levy flight.

The Levy distribution is defined by two parameters $\alpha$ and $\beta$ . The Gaussian distribution is special case of Levy distribution with $\alpha=2$ and $\beta=0$ .

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

Example Usage¶

The following example produce 1000 samples of Levy walk created from 500 samples of Levy noise (ns=500) located (mean value) at 0 (position), with characteristic exponent index of 1.4 (alpha), skeewness of 0 (beta) and diffusion of 1. (sigma).

import signalz
x = signalz.levy_walk(1000, ns=500, alpha=1.4, beta=0., sigma=1., position=0)

Function Documentation¶

signalz.generators.levy_walk.levy_walk(n, ns=0, alpha=2.0, beta=1.0, sigma=1.0, position=0.0)[source]¶

This function produces Levy walk.

Args:

n - length of the output data (int) - how many samples will be on output
ns - number of points (int) in original noise before interpolation, this number cannot be higher than desired length of data; if it is set to 0, then ns=n is used; this number is related to number of direction changes in resulting walk

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 walk (1d array)