Frechet distribution
Density, distribution function, quantile function and random generation for the Frechet distribution.
dfrechet(x, lambda = 1, mu = 0, sigma = 1, log = FALSE) pfrechet(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) qfrechet(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE) rfrechet(n, lambda = 1, mu = 0, sigma = 1)
x, q |
vector of quantiles. |
lambda, sigma, mu |
shape, scale, and location parameters. Scale and shape must be positive. |
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/σ * ((x-μ)/σ)^(-1-λ) * exp(-((x-μ)/σ)^-λ)
Cumulative distribution function
F(x) = exp(-((x-μ)/σ)^-λ)
Quantile function
F^-1(p) = μ + σ * -log(p)^{-1/λ}
Bury, K. (1999). Statistical Distributions in Engineering. Cambridge University Press.
x <- rfrechet(1e5, 5, 2, 1.5) xx <- seq(0, 1000, by = 0.1) hist(x, 200, freq = FALSE) lines(xx, dfrechet(xx, 5, 2, 1.5), col = "red") hist(pfrechet(x, 5, 2, 1.5)) plot(ecdf(x)) lines(xx, pfrechet(xx, 5, 2, 1.5), col = "red", lwd = 2)
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