logLogistic
logLogistic, function
def pure logLogistic(alpha: number, beta: number): ranvar
Returns the log-logistic distribution over $\mathbb{N}$ with parameters
alpha (scale) and beta (shape).
alpha: scale parameter, must be positive.beta: shape parameter, must be positive.
Examples
r = logLogistic(5, 2)
show table "Log-logistic" with
mean(r) as "Mean"
This produces the following table:
| Mean |
|---|
| 7.344149 |
Remarks
Inputs must be strictly positive.
The probability distribution over $\mathbb{N}$ obtained from the CDF of the log-logistic distribution is: $$P_{\alpha,\beta}[X = n] = F(n+1; \alpha,\beta) - F(n; \alpha,\beta) $$