The truncated Frechet distribution
Density, distribution function, quantile function and random generation for the truncated Fréchet distribution.
dtfrechet(x, shape, loc = 0, scale = 1, endpoint = Inf, log = FALSE) ptfrechet(x, shape, loc = 0, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) qtfrechet(p, shape, loc = 0, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) rtfrechet(n, shape, loc = 0, scale = 1, endpoint = Inf)
x |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
shape |
Shape parameter of the Fréchet distribution. |
loc |
Location parameter of the Fréchet distribution, default is 0. |
scale |
Scale parameter of the Fréchet distribution, default is 1. |
endpoint |
Endpoint of the truncated Fréchet distribution. The default value is |
log |
Logical indicating if the densities are given as \log(f), default is |
lower.tail |
Logical indicating if the probabilities are of the form P(X≤ x) ( |
log.p |
Logical indicating if the probabilities are given as \log(p), default is |
The Cumulative Distribution Function (CDF) of the truncated Fréchet distribution is equal to F_T(x) = F(x) / F(T) for x ≤ T where F is the CDF of an ordinary Fréchet distribution and T is the endpoint (truncation point) of the truncated Fréchet distribution.
dtfrechet gives the density function evaluated in x, ptfrechet the CDF evaluated in x and qtfrechet the quantile function evaluated in p. The length of the result is equal to the length of x or p.
rtfrechet returns a random sample of length n.
Tom Reynkens.
# Plot of the PDF x <- seq(1, 10, 0.01) plot(x, dtfrechet(x, shape=2, endpoint=5), xlab="x", ylab="PDF", type="l") # Plot of the CDF x <- seq(1, 10, 0.01) plot(x, ptfrechet(x, shape=2, endpoint=5), xlab="x", ylab="CDF", type="l")
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