The Laplace distribution
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The Laplace distribution is akin to two exponential
distributions spliced together.
Distribution name

Laplace
distribution

Common notation


Parameters

=
location parameter
=
scale parameter ()

Domain


Probability density
function


Cumulative distribution
function


Mean


Variance


Skewness


(Excess) kurtosis


Characteristic function


Other comments

The median and mode are . The
inverse cdf (i.e. quantile) function is .
If and then .
It is sometimes referred to as the double exponential
distribution (but this term is also apparently also used sometimes of the
Gumbel distribution)

Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “laplace”. For
details of other supported probability distributions see here.
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