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15.3 Exponentially Modified Normal Distribution

15.3.1 Probability Density Function

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

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.