Pareto distribution
Density, distribution function, quantile function and random generation for the Pareto distribution.
dpareto(x, a = 1, b = 1, log = FALSE) ppareto(q, a = 1, b = 1, lower.tail = TRUE, log.p = FALSE) qpareto(p, a = 1, b = 1, lower.tail = TRUE, log.p = FALSE) rpareto(n, a = 1, b = 1)
x, q |
vector of quantiles. |
a, b |
positive valued scale and location parameters. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x]. |
p |
vector of probabilities. |
n |
number of observations. If |
Probability density function
f(x) = (a*b^a) / x^(a+1)
Cumulative distribution function
F(x) = 1 - (b/x)^a
Quantile function
F^-1(p) = b/(1-p)^(1-a)
Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC
x <- rpareto(1e5, 5, 16) hist(x, 100, freq = FALSE) curve(dpareto(x, 5, 16), 0, 200, col = "red", add = TRUE) hist(ppareto(x, 5, 16)) plot(ecdf(x)) curve(ppareto(x, 5, 16), 0, 200, col = "red", lwd = 2, add = TRUE)
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