This is an old version, view current version.

17.3 Exponentially modified normal distribution

17.3.1 Probability density function

If μR, σR+, and λR+, then for yR, ExpModNormal(y|μ,σ,λ)=λ2 exp(λ2(2μ+λσ22y))erfc(μ+λσ2y2σ).

17.3.2 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

17.3.3 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