logLogistic
logLogistic(alpha: number, beta: number) 🡒 ranvar, pure function
Returns a probability distribution over $\mathbb{N}$ obtained from the CDF of the log-logistic distribution with:
$$P_{\alpha,\beta}[X = n] = F(n+1; \alpha,\beta) - F(n; \alpha,\beta) $$
where
$$F(x; \alpha, \beta) = { 1 \over 1+(x/\alpha)^{-\beta} }$$
The arguments alpha and beta must be positive or the function fails.
Example:
table T = with
[| as Alpha, as Beta |]
[| 0.5, 2.0 |]
[| 1.5, 2.0 |]
[| 5.5, 2.0 |]
[| 10.0, 2.0 |]
show table "" a1c4 with
T.Alpha
T.Beta
logLogistic(T.Alpha, T.Beta)