The exponential distribution
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The exponential distribution describes the time between
events if these events follow a Poisson process (i.e. a stochastic process in
which events occur continuously and independently of one another). It is also
called the negative exponential distribution. It is not the same as the
exponential family of distributions.
Distribution name

Exponential
distribution

Common notation


Parameters

=
inverse scale (i.e. rate) parameter ()

Domain


Probability density
function


Cumulative distribution
function


Mean


Variance


Skewness


(Excess) kurtosis


Characteristic function


Other comments

The exponential distribution is a special case of the Gamma distribution,
as if then .
The mode of an exponential distribution is 0. The quantile
function, i.e. the inverse cumulative distribution function, is .
The noncentral moments ( are
. Its median is .

Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “exponential”.
Functions relating to a generalised version of this distribution including an
additional location (i.e. shift) parameter may be accessed by using a DistributionName
of “exponential2” ”, see also including
additional shift and scale parameters. For details of other supported probability
distributions see here.
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