Lomax distribution
Density, distribution function, quantile function and random generation for the Lomax distribution.
dlomax(x, lambda, kappa, log = FALSE) plomax(q, lambda, kappa, lower.tail = TRUE, log.p = FALSE) qlomax(p, lambda, kappa, lower.tail = TRUE, log.p = FALSE) rlomax(n, lambda, kappa)
x, q |
vector of quantiles. |
lambda, kappa |
positive valued 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) = λ*κ / (1+λ*x)^(κ+1)
Cumulative distribution function
F(x) = 1-(1+λ*x)^-κ
Quantile function
F^-1(p) = ((1-p)^(-1/κ)-1) / λ
x <- rlomax(1e5, 5, 16) hist(x, 100, freq = FALSE) curve(dlomax(x, 5, 16), 0, 1, col = "red", add = TRUE, n = 5000) hist(plomax(x, 5, 16)) plot(ecdf(x)) curve(plomax(x, 5, 16), 0, 1, col = "red", lwd = 2, add = TRUE)
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