ReIns (version 1.0.10)

tPareto: The truncated Pareto distribution

Description

Density, distribution function, quantile function and random generation for the truncated Pareto distribution.

Usage

dtpareto(x, shape, scale = 1, endpoint = Inf, log = FALSE)
ptpareto(x, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtpareto(p, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtpareto(n, shape, scale = 1, endpoint = Inf)

Value

dtpareto gives the density function evaluated in \(x\), ptpareto the CDF evaluated in \(x\) and qtpareto the quantile function evaluated in \(p\). The length of the result is equal to the length of \(x\) or \(p\).

rtpareto returns a random sample of length \(n\).

Arguments

x

Vector of quantiles.

p

Vector of probabilities.

n

Number of observations.

shape

The shape parameter of the truncated Pareto distribution, a strictly positive number.

scale

The scale parameter of the truncated Pareto distribution, a strictly positive number. Its default value is 1.

endpoint

Endpoint of the truncated Pareto distribution. The default value is Inf for which the truncated Pareto distribution corresponds to the ordinary Pareto distribution.

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.

Author

Tom Reynkens

Details

The Cumulative Distribution Function (CDF) of the truncated Pareto distribution is equal to \(F_T(x) = F(x) / F(T)\) for \(x \le T\) where \(F\) is the CDF of an ordinary Pareto distribution and \(T\) is the endpoint (truncation point) of the truncated Pareto distribution.

See Also

Pareto, Distributions

Examples

# Plot of the PDF
x = seq(1,10,0.01)
plot(x, dtpareto(x, shape=2, endpoint=10), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x = seq(1,10,0.01)
plot(x, ptpareto(x, shape=2, endpoint=10), xlab="x", ylab="CDF", type="l")