r6qualitytools (version 1.0.1)

dweibull3: dweibull3: The Weibull Distribution (3 Parameter)

Description

Density function, distribution function, and quantile function for the Weibull distribution with a threshold parameter.

Usage

dweibull3(x, shape, scale, threshold)

Value

dweibull3 returns the density, pweibull3 returns the distribution function, and qweibull3 returns the quantile function for the Weibull distribution with a threshold.

Arguments

x

A numeric vector of quantiles.

shape

The shape parameter of the Weibull distribution. Default is 1.

scale

The scale parameter of the Weibull distribution. Default is 1.

threshold

The threshold (or location) parameter of the Weibull distribution. Default is 0.

Details

The Weibull distribution with the scale parameter alpha, shape parameter c, and threshold parameter zeta has a density function given by: $$f(x) = \frac{c}{\alpha} \left(\frac{x - \zeta}{\alpha}\right)^{c-1} \exp\left(-\left(\frac{x - \zeta}{\alpha}\right)^c\right)$$

The cumulative distribution function is given by: $$F(x) = 1 - \exp\left(-\left(\frac{x - \zeta}{\alpha}\right)^c\right)$$

Examples

dweibull3(x = 1, scale = 1, shape = 5, threshold = 0)
temp <- pweibull3(q = 1, scale = 1, shape = 5, threshold = 0)
temp
qweibull3(p = temp, scale = 1, shape = 5, threshold = 0)