The continuous power-law distribution
Density and distribution function of the continuous power-law distribution, with parameters xmin and alpha.
dplcon(x, xmin, alpha, log = FALSE) pplcon(q, xmin, alpha, lower.tail = TRUE) rplcon(n, xmin, alpha)
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 ≤ x], otherwise, P[X > x]. |
n |
Number of observations. If |
dplcon gives the denisty and pplcon gives the distribution function.
The discrete random number generator is very inefficient
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")
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