Student's t-distribution

Also known as Student's distribution, t-distribution

probability distribution

In the Vinony graph

Vinony's link graph records 370 inbound references to Student's t-distribution, and connects out to median, resampling and variance.

Vinony links it to 39 Wikipedia language editions.

Parameters: 0"}}'> ν > 0 {\displaystyle \nu >0} degrees of freedom ( real , nearly always a positive integer )
Support: x ∈ ( − ∞ , ∞ ) {\displaystyle x\in (-\infty ,\infty )}
Pdf: Γ ( ν + 1 2 ) π ν Γ ( ν 2 ) ( 1 + x 2 ν ) − ν + 1 2 {\displaystyle {\frac {\Gamma {\left({\frac {\nu +1}{2}}\right)}}{{\sqrt {\pi \nu }}\,\Gamma {\left({\frac {\nu }{2}}\right)}}}\left(1+{\frac {x^{2}}{\nu }}\right)^{-{\frac {\nu +1}{2}}}}
Mean: 0 {\displaystyle 0} for 1,"}}'> ν > 1 , {\displaystyle \nu >1,} otherwise undefined
Median: 0 {\displaystyle 0}
Mode: 0 {\displaystyle 0}
Variance: ν ν − 2 {\displaystyle {\frac {\nu }{\nu -2}}} for 2,"}}'> ν > 2 , {\displaystyle \nu >2,} ∞ {\displaystyle \infty } for 1 < ν ≤ 2 , {\displaystyle 1<\nu \leq 2,} otherwise undefined
Skewness: 0 {\displaystyle 0} for 3\\ ,"}}'> ν > 3 , {\displaystyle \ \nu >3\ ,} otherwise undefined
Excess kurtosis: 6 ν − 4 {\displaystyle {\frac {6}{\nu -4}}} for 4,"}}'> ν > 4 , {\displaystyle \nu >4,} ∞ {\displaystyle \infty } for 2 < ν ≤ 4 , {\displaystyle 2<\nu \leq 4,} otherwise undefined
Mgf: undefined