pymc.AsymmetricLaplace#
- class pymc.AsymmetricLaplace(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)[source]#
Asymmetric-Laplace log-likelihood.
The pdf of this distribution is
\[\begin{split}{f(x|\\b,\kappa,\mu) = \left({\frac{\\b}{\kappa + 1/\kappa}}\right)\,e^{-(x-\mu)\\b\,s\kappa ^{s}}}\end{split}\]where
\[s = sgn(x-\mu)\]Support
\(x \in \mathbb{R}\)
Mean
\(\mu-\frac{\\\kappa-1/\kappa}b\)
Variance
\(\frac{1+\kappa^{4}}{b^2\kappa^2 }\)
AsymmetricLaplace distribution can be parameterized either in terms of kappa or q. The link between the two parametrizations is given by
\[\kappa = \sqrt(\frac{q}{1-q})\]- Parameters:
- kappatensor_like of
float Symmetry parameter (kappa > 0).
- mutensor_like of
float Location parameter.
- btensor_like of
float Scale parameter (b > 0).
- qtensor_like of
float Symmetry parameter (0 < q < 1).
- kappatensor_like of
Notes
The parametrization in terms of q is useful for quantile regression with q being the quantile of interest.
Methods
AsymmetricLaplace.dist([kappa, mu, b, q])Creates a tensor variable corresponding to the cls distribution.