pweibull3 {r6qualitytools} | R Documentation |
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)