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19.11 Log-logistic distribution

19.11.1 Probability density function

If \(\alpha, \beta \in \mathbb{R}^+\), then for \(y \in \mathbb{R}^+\), \[ \text{Log-Logistic}(y|\alpha,\beta) = \frac{\ \left(\frac{\beta}{\alpha}\right) \left(\frac{y}{\alpha}\right)^{\beta-1}\ }{\left(1 + \left(\frac{y}{\alpha}\right)^\beta\right)^2} . \]

19.11.2 Sampling statement

y ~ loglogistic(alpha, beta)

Increment target log probability density with unnormalized version of loglogistic_lpdf(y | alpha, beta)
Available since 2.29

19.11.3 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