pweibull3: pweibull3: The Weibull Distribution (3 Parameter)

In r6qualitytools: R6-Based Statistical Methods for Quality Science

pweibull3: The Weibull Distribution (3 Parameter)

Description

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

Usage

pweibull3(q, shape, scale, threshold)

Arguments

q	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)

Value

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

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)

r6qualitytools documentation built on Oct. 4, 2024, 1:09 a.m.