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16.4 Skew normal distribution

16.4.1 Probability density function

If ξR, ωR+, and αR, then for yR, SkewNormal(yξ,ω,α)=1ω2π exp(12(yξω)2) (1+erf(α(yξω2))).

16.4.2 Sampling statement

y ~ skew_normal(xi, omega, alpha)

Increment target log probability density with skew_normal_lupdf(y | xi, omega, alpha).

16.4.3 Stan functions

real skew_normal_lpdf(reals y | reals xi, reals omega, reals alpha)
The log of the skew normal density of y given location xi, scale omega, and shape alpha

real skew_normal_lupdf(reals y | reals xi, reals omega, reals alpha)
The log of the skew normal density of y given location xi, scale omega, and shape alpha dropping constant additive terms

real skew_normal_cdf(reals y, reals xi, reals omega, reals alpha)
The skew normal distribution function of y given location xi, scale omega, and shape alpha

real skew_normal_lcdf(reals y | reals xi, reals omega, reals alpha)
The log of the skew normal cumulative distribution function of y given location xi, scale omega, and shape alpha

real skew_normal_lccdf(reals y | reals xi, reals omega, reals alpha)
The log of the skew normal complementary cumulative distribution function of y given location xi, scale omega, and shape alpha

R skew_normal_rng(reals xi, reals omega, real alpha)
Generate a skew normal variate with location xi, scale omega, and shape alpha; may only be used in transformed data and generated quantities blocks. For a description of argument and return types, see section vectorized PRNG functions.