19.3 Exponentially modified normal distribution
19.3.1 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).
19.3.2 Sampling statement
y ~
exp_mod_normal
(mu, sigma, lambda)
Increment target log probability density with exp_mod_normal_lupdf(y | mu, sigma, lambda)
.
Available since 2.0
19.3.3 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
Available since 2.18
real
exp_mod_normal_lupdf
(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 dropping constant additive terms
Available since 2.25
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
Available since 2.0
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
Available since 2.18
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
Available since 2.18
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.
Available since 2.18