Create a Levy-Pareto flight — flight

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.

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]

Value

A data frame with ndims columns and N rows.

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.

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)
#> Warning: Not a Levy-Pareto distribution if alpha <= 1 or alpha >= 2
plot(density(diff(df$dim1)))

plot(df$dim1, df$dim2, type = "l")