poweRlaw (version 0.80.0)

dplcon: The continuous power-law distribution

Description

Density and distribution function of the continuous power-law distribution, with parameters xmin and alpha.

Usage

dplcon(x, xmin, alpha, log = FALSE)
pplcon(q, xmin, alpha, lower.tail = TRUE)
rplcon(n, xmin, alpha)

Value

dplcon gives the denisty and pplcon gives the distribution function.

Arguments

x, q

vector of quantiles. The discrete power-law distribution is defined for x > xmin

xmin

The lower bound of the power-law distribution. For the continuous power-law, xmin >= 0. for the discrete distribution, xmin > 0.

alpha

The scaling parameter: alpha > 1.

log

logical (default FALSE) if TRUE, log values are returned.

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

n

Number of observations. If length(n) > 1, the length is taken to be the number required.

Examples

xmin = 1; alpha = 1.5
x = seq(xmin, 10, length.out=1000)
plot(x, dplcon(x, xmin, alpha), type="l")
plot(x, pplcon(x, xmin, alpha), type="l", main="Distribution function")
n = 1000
con_rns = rplcon(n, xmin, alpha)
con_rns = sort(con_rns)
p = rep(1/n, n)
#Zipfs plot
plot(con_rns, rev(cumsum(p)), log="xy", type="l")