15.3 Exponentially Modified Normal Distribution
15.3.1 Probability Density Function
If μ∈R, σ∈R+, and λ∈R+, then for y∈R, ExpModNormal(y|μ,σ,λ)=λ2 exp(λ2(2μ+λσ2−2y))erfc(μ+λσ2−y√2σ).
15.3.2 Sampling Statement
y ~
exp_mod_normal
(mu, sigma, lambda)
Increment target log probability density with exp_mod_normal_lpdf(y | mu, sigma, lambda)
dropping constant additive terms.
15.3.3 Stan Functions
real
exp_mod_normal_lpdf
(reals y | reals mu, reals sigma, reals lambda)
The log of the exponentially modified normal density of y given
location mu, scale sigma, and shape lambda
real
exp_mod_normal_cdf
(reals y, reals mu, reals sigma, reals lambda)
The exponentially modified normal cumulative distribution function of
y given location mu, scale sigma, and shape lambda
real
exp_mod_normal_lcdf
(reals y | reals mu, reals sigma, reals lambda)
The log of the exponentially modified normal cumulative distribution
function of y given location mu, scale sigma, and shape lambda
real
exp_mod_normal_lccdf
(reals y | reals mu, reals sigma, reals lambda)
The log of the exponentially modified normal complementary cumulative
distribution function of y given location mu, scale sigma, and shape
lambda
R
exp_mod_normal_rng
(reals mu, reals sigma, reals lambda)
Generate a exponentially modified normal variate with location mu,
scale sigma, and shape lambda; may only be used in transformed data and generated
quantities blocks. For a description of argument and return types, see
section vectorized PRNG functions.