Student's t

155. Student's t

155.1. t-Distribution

𝑓 (𝑡 | 𝜈) = \frac{Γ (\frac{𝜈 + 1}{2})}{\sqrt{𝜈 𝜋} Γ (\frac{𝜈}{2})} {(1 + \frac{𝑡^{2}}{𝜈})}^{- \frac{𝜈 + 1}{2}}

Where:

$𝑡$ : t-statistic
$𝜈$ (or $𝑑 𝑓$ ): degrees of freedom
$Γ$ : Gamma function (generalizes the factorial function)

Continuous probability distribution for estimating the mean of a normally distributed population in situations where:

Sample size is small
Population standard deviation is unknown

Similar in shape to the normal distribution but has heavier tails, which means it gives more probability to values further from the mean