tGPD function

The truncated generalised Pareto distribution

Density, distribution function, quantile function and random generation for the truncated Generalised Pareto Distribution (GPD).

dtgpd(x, gamma, mu = 0, sigma, endpoint = Inf, log = FALSE)
ptgpd(x, gamma, mu = 0, sigma, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtgpd(p, gamma, mu = 0, sigma, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtgpd(n, gamma, mu = 0, sigma, endpoint = Inf)

Arguments

• x: Vector of quantiles.
• p: Vector of probabilities.
• n: Number of observations.
• gamma: The $\gamma$ parameter of the GPD, a real number.
• mu: The $\mu$ parameter of the GPD, a strictly positive number. Default is 0.
• sigma: The $\sigma$ parameter of the GPD, a strictly positive number.
• endpoint: Endpoint of the truncated GPD. The default value is Inf for which the truncated GPD corresponds to the ordinary GPD.
• 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 GPD is equal to $F_T(x) = F(x) / F(T)$ for $x \le T$ where $F$ is the CDF of the ordinary GPD and $T$ is the endpoint (truncation point) of the truncated GPD.

Returns

dtgpd gives the density function evaluated in $x$, ptgpd the CDF evaluated in $x$ and qtgpd the quantile function evaluated in $p$. The length of the result is equal to the length of $x$ or $p$.

rtgpd returns a random sample of length $n$.

Author(s)

Tom Reynkens

See Also

tGPD, Pareto, Distributions

Examples

# Plot of the PDF
x <- seq(0, 10, 0.01)
plot(x, dtgpd(x, gamma=1/2, sigma=5, endpoint=8), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(0, 10, 0.01)
plot(x, ptgpd(x, gamma=1/2, sigma=5, endpoint=8), xlab="x", ylab="CDF", type="l")