clauset.xmax {distributionsrd}

Pareto scale determination à la Clauset

Description

This method determines the optimal scale parameter of the Inverse Pareto distribution using the iterative method (Clauset et al. 2009) that minimizes the Kolmogorov-Smirnov distance.

Usage

clauset.xmax(x, q = 1)

Arguments

x

data vector

q

Percentage of data to search over (starting from the smallest values)

Value

Returns a named list containing a

coefficients

Named vector of coefficients

KS

Minimum Kolmogorov-Smirnov distance

n

Number of observations in the Inverse Pareto tail

coeff.evo

Evolution of the Inverse Pareto shape parameter over the iterations

References

Clauset A, Shalizi CR, Newman ME (2009). “Power-law distributions in empirical data.” SIAM review, 51(4), 661–703.

Examples

## Determine cuttof from compostie InvPareto-Lognormal distribution using Clauset's method
dist <- c("invpareto", "lnorm")
coeff <- c(coeff1.k = 1.5, coeff2.meanlog = 1, coeff2.sdlog = 0.5)
x <- rcomposite(1e3, dist = dist, coeff = coeff)
out <- clauset.xmax(x = x)
out$coefficients
coeffcomposite(dist = dist, coeff = coeff, startc = c(1, 1))$coeff1

## Speed up method by considering values above certain quantile only
dist <- c("invpareto", "lnorm")
coeff <- c(coeff1.k = 1.5, coeff2.meanlog = 1, coeff2.sdlog = 0.5)
x <- rcomposite(1e3, dist = dist, coeff = coeff)
out <- clauset.xmax(x = x, q = 0.5)
out$coefficients
coeffcomposite(dist = dist, coeff = coeff, startc = c(1, 1))$coeff1