= Student's t Distribution =

'''Student's t distribution''' is a bell-shaped continuous probability distribution function that is centered on zero and parameterized to [[Statistics/DegreesOfFreedom|degrees of freedom]].

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== Description ==

When working with [[Analysis/NormalDistribution|normally distributed]] data where the sample [[Analysis/Variance|variance]] is not an appropriate estimator for population variance, Student's t distribution is more appropriate. The distribution has fatter tails and is effectively a more conservative fit to normal data. More formally, the variance is greater than 1 but converges to 1 as the sample size (''n'') grows.

The probability density function is given as:

{{attachment:pdf.svg}}

where ''Γ(.)'' is the [[Analysis/GammaFunction|gamma function]] and ''d'' is the number of [[Statistics/DegreesOfFreedom|degrees of freedom]] (i.e., ''n - 1'').



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CategoryRicottone