Median parameterization of the Weibull pdf.
Usage
dweibull_median(x, mu, k, log = FALSE)
Arguments
- x
Value space, x > 0.
- mu
Median parameter, mu > 0.
- k
Shape parameter, k > 0.
- log
Optional argument. If TRUE, returns log(pdf). Normally False.
Details
Define constant sigma as
$$\sigma(\mu, k) := \mu / \Gamma(1 + 1 / k)$$
The Weibull distribution density is defined as
$$f(y) = \frac{k}{\sigma} * (\frac{x}{\sigma})^{\alpha - 1} * exp(-(\frac{x}{\sigma})^\alpha)$$
Examples
x <- seq(from = 0.01, to = 10, length.out = 1000)
plot(x, dweibull_median(x, mu = 2, k = 1), type = "l")
