dweibull3: The Weibull Distribution (3 Parameter)

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

Usage

dweibull3(x, shape, scale, 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.

Value

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

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)
#> [1] 1.839397
temp <- pweibull3(q = 1, scale = 1, shape = 5, threshold = 0)
temp
#> [1] 0.6321206
qweibull3(p = temp, scale = 1, shape = 5, threshold = 0)
#> [1] 0.9999999