loglogistic

loglogistic(alpha: number, beta: number) 🡒 ranvar, pure function

Returns a probability distribution over $\mathbb{Z}$ obtained from the CDF of the log-logistic distribution with:

$$P_{\alpha,\beta}[X = n] = F(n; \alpha,\beta) - F(n - 1; \alpha,\beta) $$

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)

See also