ReIns (version 1.0.10)

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 \(\alpha\) parameter of the truncated Burr distribution, a strictly positive number.

rho

The \(\rho\) parameter of the truncated Burr distribution, a strictly negative number.

eta

The \(\eta\) 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 \(P(X\le x)\) (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 Burr distribution is equal to \(F_T(x) = F(x) / F(T)\) for \(x \le T\) where \(F\) is the CDF of the ordinary Burr distribution and \(T\) is the endpoint (truncation point) of the truncated Burr distribution.

See Also

Burr, Distributions

Examples

# 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")