The Laplace distribution with location loc and scale parameters.

Inherits From: Distribution

Mathematical details

The probability density function (pdf) of this distribution is,

pdf(x; mu, sigma) = exp(-|x - mu| / sigma) / Z
Z = 2 sigma

where loc = mu, scale = sigma, and Z is the normalization constant.

Note that the Laplace distribution can be thought of two exponential distributions spliced together "back-to-back."

The Lpalce distribution is a member of the location-scale family, i.e., it can be constructed as,

X ~ Laplace(loc=0, scale=1)
Y = loc + scale * X