The Chisquared distribution
[this page  pdf  back links]
The chisquared distribution with degrees
of freedom is the distribution of a sum of the squares of independent
standard normal random variables. A consequence is that the sum of independent
chisquared variables is also chisquared distributed. It is widely used in
hypothesis testing, goodness of fit analysis or in constructing confidence
intervals. It is a special case of the gamma distribution.
Distribution name

Chisquared
distribution

Common notation


Parameters

=
degrees of freedom (positive integer)

Domain


Probability density
function


Cumulative distribution
function


Mean


Variance


Skewness


(Excess) kurtosis


Characteristic function


Other comments

Its median is approximately . Its mode is . Is also known as the
central chisquared distribution (when there is a need to contrast it with
the noncentral chisquared distribution).
In the special case of the cumulative
distribution function simplifies to .
As , and

Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “chisquared”.
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 “chisquared3” ”, see also including
additional shift and scale parameters. For details of other supported
probability distributions see here.
NAVIGATION LINKS
Contents  Prev  Next