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16.1 Lognormal Distribution

16.1.1 Probability Density Function

If μR and σR+, then for yR+, LogNormal(y|μ,σ)=12π σ1y exp(12(logyμσ)2).

16.1.2 Sampling Statement

y ~ lognormal(mu, sigma)

Increment target log probability density with lognormal_lpdf( y | mu, sigma) dropping constant additive terms.

16.1.3 Stan Functions

real lognormal_lpdf(reals y | reals mu, reals sigma)
The log of the lognormal density of y given location mu and scale sigma

real lognormal_cdf(reals y, reals mu, reals sigma)
The cumulative lognormal distribution function of y given location mu and scale sigma

real lognormal_lcdf(reals y | reals mu, reals sigma)
The log of the lognormal cumulative distribution function of y given location mu and scale sigma

real lognormal_lccdf(reals y | reals mu, reals sigma)
The log of the lognormal complementary cumulative distribution function of y given location mu and scale sigma

R lognormal_rng(reals mu, reals sigma)
Generate a lognormal 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.