Pareto function

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)

Arguments

• 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 1.
• log: Logical indicating if the densities are given as $\log(f)$, default is FALSE.
• lower.tail: Logical indicating if the probabilities are of the form $P(X\le x)$ (TRUE) or $P(X>x)$ (FALSE). Default is TRUE.
• log.p: Logical indicating if the probabilities are given as $\log(p)$, default is FALSE.

Details

The Cumulative Distribution Function (CDF) of the Pareto distribution is equal to $F(x) = 1-(x/scale)^{-shape}$ for all $x \ge scale$ and $F(x)=0$ otherwise. Both shape and scale need to be strictly positive.

Returns

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 $n$.

Author(s)

Tom Reynkens.

See Also

tPareto, GPD, Distributions

Examples

# 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")