tBurr: The truncated Burr distribution

Description

Density, distribution function, quantile function and random generation for the truncated Burr distribution (type XII).

Usage

dtburr(x, alpha, rho, eta = 1, endpoint = Inf, log = FALSE)
ptburr(x, alpha, rho, eta = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtburr(p, alpha, rho, eta = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtburr(n, alpha, rho, eta = 1, endpoint = Inf)

Value

dtburr gives the density function evaluated in $x$ , ptburr the CDF evaluated in $x$ and qtburr the quantile function evaluated in $p$ . The length of the result is equal to the length of $x$ or $p$ .

rtburr returns a random sample of length $n$ .

Arguments

x: Vector of quantiles.
p: Vector of probabilities.
n: Number of observations.
alpha: The $α$ parameter of the truncated Burr distribution, a strictly positive number.
rho: The $ρ$ parameter of the truncated Burr distribution, a strictly negative number.
eta: The $η$ parameter of the truncated Burr distribution, a strictly positive number. The default value is 1.
endpoint: Endpoint of the truncated Burr distribution. The default value is Inf for which the truncated Burr distribution corresponds to the ordinary Burr 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 $P (X \leq x)$ (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 Burr distribution is equal to $F_{T} (x) = F (x) / F (T)$ for $x \leq T$ where $F$ is the CDF of the ordinary Burr distribution and $T$ is the endpoint (truncation point) of the truncated Burr distribution.

Examples

Run this code

# Plot of the PDF
x <- seq(0, 10, 0.01)
plot(x, dtburr(x, alpha=2, rho=-1, endpoint=9), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(0, 10, 0.01)
plot(x, ptburr(x, alpha=2, rho=-1, endpoint=9), xlab="x", ylab="CDF", type="l")

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