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## 17.10 Skew double exponential distribution

### 17.10.1 Probability density function

If $$\mu \in \mathbb{R}$$, $$\sigma \in \mathbb{R}^+$$ and $$\tau \in [0, 1]$$, then for $$y \in \mathbb{R}$$, \begin{aligned} & \text{SkewDoubleExponential} (y|\mu,\sigma, \tau) = \\ & \qquad \qquad \frac{2 \tau (1 - \tau) }{\sigma} \exp \left[ - \frac{2}{\sigma} \left[ \left(1 - \tau \right) I(y < \mu) (\mu - y) + \tau I(y > \mu)(y-\mu) \right] \right] \end{aligned}

### 17.10.2 Sampling statement

y ~ skew_double_exponential(mu, sigma, tau)

Increment target log probability density with skew_double_exponential(y | mu, sigma, tau)
Available since 2.28

### 17.10.3 Stan functions

real skew_double_exponential_lpdf(reals y | reals mu, reals sigma, reals tau)
The log of the skew double exponential density of y given location mu, scale sigma and skewness tau
Available since 2.28

real skew_double_exponential_lupdf(reals y | reals mu, reals sigma, reals tau)
The log of the skew double exponential density of y given location mu, scale sigma and skewness tau dropping constant additive terms
Available since 2.28

real skew_double_exponential_cdf(reals y, reals mu, reals sigma, reals tau)
The skew double exponential cumulative distribution function of y given location mu, scale sigma and skewness tau
Available since 2.28

real skew_double_exponential_lcdf(reals y | reals mu, reals sigma, reals tau)
The log of the skew double exponential cumulative distribution function of y given location mu, scale sigma and skewness tau
Available since 2.28

real skew_double_exponential_lccdf(reals y | reals mu, reals sigma, reals tau)
The log of the skew double exponential complementary cumulative distribution function of y given location mu, scale sigma and skewness tau
Available since 2.28

R skew_double_exponential_rng(reals mu, reals sigma, reals tau)
Generate a skew double exponential variate with location mu, scale sigma and skewness tau; 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 2.28