16.8 Logistic distribution
16.8.1 Probability density function
If μ∈R and σ∈R+, then for y∈R, Logistic(y|μ,σ)=1σ exp(−y−μσ) (1+exp(−y−μσ))−2.
16.8.2 Sampling statement
y ~
logistic
(mu, sigma)
Increment target log probability density with logistic_lupdf(y | mu, sigma)
.
16.8.3 Stan functions
real
logistic_lpdf
(reals y | reals mu, reals sigma)
The log of the logistic density of y given location mu and scale sigma
real
logistic_lupdf
(reals y | reals mu, reals sigma)
The log of the logistic density of y given location mu and scale sigma
dropping constant additive terms
real
logistic_cdf
(reals y, reals mu, reals sigma)
The logistic cumulative distribution function of y given location mu
and scale sigma
real
logistic_lcdf
(reals y | reals mu, reals sigma)
The log of the logistic cumulative distribution function of y given
location mu and scale sigma
real
logistic_lccdf
(reals y | reals mu, reals sigma)
The log of the logistic complementary cumulative distribution function
of y given location mu and scale sigma
R
logistic_rng
(reals mu, reals sigma)
Generate a logistic variate with location mu and scale sigma; may only
be used in transformed data and generated quantities blocks.
For a description of argument and return types, see section
vectorized PRNG functions.