ReIns (version 1.0.10)

tWeibull: The truncated Weibull distribution

Description

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

Usage

dtweibull(x, shape, scale = 1, endpoint = Inf, log = FALSE)
ptweibull(x, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtweibull(p, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtweibull(n, shape, scale = 1, endpoint = Inf)

Value

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

rtweibull 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 Weibull distribution, a strictly positive number.

scale

The scale parameter of the Weibull distribution, a strictly positive number, default is 1.

endpoint

Endpoint of the truncated Weibull distribution. The default value is Inf for which the truncated Weibull distribution corresponds to the ordinary Weibull 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 Weibull distribution is equal to \(F_T(x) = F(x) / F(T)\) for \(x \le T\) where \(F\) is the CDF of the ordinary Weibull distribution and \(T\) is the endpoint (truncation point) of the truncated Weibull distribution.

See Also

Weibull, Distributions

Examples

# Plot of the PDF
x <- seq(0, 10, 0.01)
plot(x, dtweibull(x, shape=2, scale=0.5, endpoint=1), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(0, 10, 0.01)
plot(x, ptweibull(x, shape=2, scale=0.5, endpoint=1), xlab="x", ylab="CDF", type="l")