The Pareto distribution
Density, distribution function, quantile function and random generation for the Pareto distribution (type I).
dpareto(x, shape, scale = 1, log = FALSE) ppareto(x, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) qpareto(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) rpareto(n, shape, scale = 1)
x |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
shape |
The shape parameter of the Pareto distribution, a strictly positive number. |
scale |
The scale parameter of the Pareto distribution, a strictly positive number. Its 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 Pareto distribution is equal to
F(x) = 1-(x/scale)^{-shape} for all x ≥ scale and F(x)=0 otherwise. Both shape and scale need to be strictly positive.
dpareto gives the density function evaluated in x, ppareto the CDF evaluated in x and qpareto the quantile function evaluated in p. The length of the result is equal to the length of x or p.
rpareto returns a random sample of length n.
Tom Reynkens.
# Plot of the PDF x <- seq(1, 10, 0.01) plot(x, dpareto(x, shape=2), xlab="x", ylab="PDF", type="l") # Plot of the CDF x <- seq(1, 10, 0.01) plot(x, ppareto(x, shape=2), xlab="x", ylab="CDF", type="l")
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