Student's t-distribution
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probability distribution
Key facts
- Parameters
- 0"}}'> ν > 0 {\displaystyle \nu >0} degrees of freedom ( real , nearly always a positive integer )
- Support
- x ∈ ( − ∞ , ∞ ) {\displaystyle x\in (-\infty ,\infty )}
- 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
via Wikipedia infobox
Wikidata facts
- Subclass of
- continuous probability distribution
- Named after
- William Sealy Gosset
Show 4 more facts
- Commons category
- Student's t-distribution
- discoverer or inventor
- William Sealy Gosset
- on focus list of Wikimedia project
- Wikipedia:Vital articles/Level/4
- maintained by WikiProject
- WikiProject Mathematics
Sources (2)
via Wikidata · CC0
~36 min read
Encyclopedic overview
In probability theory and statistics, Student's t distribution (or simply the t distribution)
t
Excerpted from Wikipedia’s “Student's t-distribution” article, available under the CC BY-SA 4.0 licence.