tPareto function

The truncated Pareto distribution

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

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)

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.

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.

Returns

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 $n$.

Author(s)

Tom Reynkens

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")