20.11 Log-logistic distribution
20.11.1 Probability density function
If \(\alpha, \beta \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{Log-Logistic}(y|\alpha,\beta) = \frac{\ \left(\frac{\beta}{\alpha}\right) \left(\frac{y}{\alpha}\right)^{\beta-1}\ }{\left(1 + \left(\frac{y}{\alpha}\right)^\beta\right)^2} . \]
20.11.2 Sampling statement
y ~ loglogistic(alpha, beta)
Increment target log probability density with unnormalized
version of loglogistic_lpdf(y | alpha, beta)
Available since 2.29
20.11.3 Stan functions
real loglogistic_lpdf(reals y | reals alpha, reals beta)
The log of the log-logistic density of y given scale alpha and shape beta
Available since 2.29
real loglogistic_cdf(reals y, reals alpha, reals beta)
The log-logistic cumulative distribution function of y given scale alpha and shape beta
Available since 2.29
R loglogistic_rng(reals alpha, reals beta)
Generate a log-logistic variate with scale alpha and shape beta; may only
be used in transformed data and generated quantities blocks.
For a description of argument and return types, see section
vectorized PRNG functions.
Available since 2.29