The Beta distribution
[this page  pdf  back links]
The beta distribution describes a distribution in which
outcomes are limited to a specific range, the probability density function
within this range being characterised by two shape parameters.
Distribution name

Beta
distribution

Common notation


Parameters

= shape
parameter (
= shape
parameter (

Domain


Probability density
function


Cumulative distribution
function


Mean


Variance


Skewness


(Excess) kurtosis


Characteristic function


Other comments

The beta distribution is also known as a beta distribution
of the first kind. Its mode is .
There is no simple closed form solution for its median.
The beta distribution parameters are sometimes taken to
include boundary parameters () in
which case its domain is , and its pdf and cdf are and
where
,
its mean is ,
its mode is for
and
its variance is
If and
then
.
If then
and
if then
(if
and
).
The ’th order statistic of a
sample of size from the uniform distribution
has a beta distribution, .
If then
,
i.e. the Pert distribution is a special case of the beta distribution.
Its noncentral moments are .

Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “beta”.
Functions relating to a generalised version of this distribution including
additional location (i.e. shift) and scale parameters may be accessed by using
a DistributionName of “beta4”, see also including
additional shift and scale parameters. For details of other supported
probability distributions see here.
NAVIGATION LINKS
Contents  Prev  Next