The Student’s t distribution
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The Student’s t distribution (more simply the t
distribution) arises when estimating the mean of a normally distributed
population when sample sizes are small and the population standard deviation is
unknown.
Distribution name
|
(Standard) Student’s
t distribution
|
Common notation
|
|
Parameters
|
=
degrees of freedom (, usually is
an integer although in some situations a non-integral can
arise)
|
Domain
|
|
Probability density
function
|
|
Cumulative distribution
function
|
where
|
Mean
|
|
Variance
|
|
Skewness
|
|
(Excess) kurtosis
|
|
Characteristic function
|
where is a Bessel function
|
Other comments
|
It is a special case of the generalised hyperbolic
distribution.
Its non-central moments if is
even and are:
If is even and then , if is
odd and then and if is
odd and then is undefined.
|
Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “student's t”.
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 “student's t3”, see also including
additional shift and scale parameters. For details of other supported
probability distributions see here.
NAVIGATION LINKS
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