Exponential distribution.

Inherits From: Gamma, Distribution

The Exponential distribution is parameterized by an event rate parameter.

Mathematical Details

The probability density function (pdf) is,

pdf(x; lambda, x > 0) = exp(-lambda x) / Z
Z = 1 / lambda

where rate = lambda and Z is the normalizaing constant.

The Exponential distribution is a special case of the Gamma distribution, i.e.,

Exponential(rate) = Gamma(concentration=1., rate)

The Exponential distribution uses a rate parameter, or "inverse scale", which can be intuited as,

X ~ Exponential(rate=1)
Y = X / rate