flight_LevyPareto: Create a Levy-Pareto flight

In FredHasselman/casnet: A Toolbox for Studying Complex Adaptive Systems and Networks

Create a Levy-Pareto flight

Description

Creates a Rayleigh flight by taking increments from the Normal distributions implemented as the stable distribution (stabledist::rstable()) with index paramter alpha = 1.5 and skewness parameter beta = 0.

Usage

flight_LevyPareto(
  N = 1000,
  ndims = 2,
  alpha = 1.5,
  beta = 0,
  scale = 1,
  location = 0
)

Arguments

N	Length of time series (default = 1000)
ndims	Number of dimensions (default = 2)
alpha	Index of stability parameter in ⁠(0,2]⁠
beta	Skewness parameter in ⁠[-1,1]⁠
scale	Scale parameterin ⁠(0,Inf)⁠
location	Location (shift) parameter in ⁠[-Inf,Inf]⁠

Details

Note that the increments are not strictly from the distribution called the Levy distribution, but rather a a Levy-with-Pareto-tail-type distribution (i.e. when ⁠1 < alpha < 2⁠). Use alpha = 1/2 and beta = 1 if the Levy distribution is required.

Value

A data frame with ndims columns and N rows.

Examples

# Levy-Pareto
df <- flight_LevyPareto()
plot(density(diff(df$dim1)))
plot(df$dim1, df$dim2, type = "l")

# "The" Levy distribution
df <- flight_LevyPareto(alpha = 1/2, beta = 1)
plot(density(diff(df$dim1)))
plot(df$dim1, df$dim2, type = "l")

FredHasselman/casnet documentation built on June 14, 2024, 6:35 p.m.