Asymmetric Laplace PDF with m = 0 in red. Note that the κ = 2 and 1/2 curves are mirror images. The κ = 1 curve in blue is the symmetric Laplace distribution.
Cumulative distribution function
Asymmetric Laplace CDF with m = 0 in red.
Parameters
location (real) scale (real)
asymmetry (real)
Support
PDF
(see article)
CDF
(see article)
Mean
Median
if
if
Variance
Skewness
Excess kurtosis
Entropy
CF
In probability theory and statistics, the asymmetric Laplace distribution (ALD) is a continuous probability distribution which is a generalization of the Laplace distribution. Just as the Laplace distribution consists of two exponential distributions of equal scale back-to-back about x = m, the asymmetric Laplace consists of two exponential distributions of unequal scale back to back about x = m, adjusted to assure continuity and normalization. The difference of two variates exponentially distributed with different means and rate parameters will be distributed according to the ALD. When the two rate parameters are equal, the difference will be distributed according to the Laplace distribution.
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