Asymmetric Laplace distribution
Continuous probability distribution / From Wikipedia, the free encyclopedia
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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.
Probability density function 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 | asymmetry (real) | ||
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Support | ;+\infty )\,} | ||
(see article) | |||
CDF | (see article) | ||
Mean | |||
Median |
if if | ||
Variance | |||
Skewness | |||
Excess kurtosis | |||
Entropy | |||
CF |