Student's t | t distribution
ProbabilitydistributionThisarticleisaboutthemathematicsofStudentst-distribution.Foritsusesinstatistics,seeStudentst-test.StudentstProbabilitydensityfunctionCumulativedistributionfunctionParametersν>0{displaystyleu>0}degreesoffreedom(real)Supportx∈(−∞,∞){displaystylexin(-infty,infty)}PDFΓ(ν+12)νπΓ(ν2)(1+x2ν)−ν+12{displaystyleextstyle{frac{Gammaleft({frac{u+1}{2}}ight)}{{sqrt{upi}},Gammaleft({frac{u}{2}}ight)}}left(1+{frac{x{2}}{u}}ight){-{frac{u+1}{2}}}!}CDF12+xΓ(ν+12)×2F1(12,ν+12;32;−x...
Probability distribution
This article is about the mathematics of Students t-distribution. For its uses in statistics, see Students t-test. Students tProbability density function
Cumulative distribution function
Parameters ν>0{displaystyle u >0} degrees of freedom (real)Support x∈(−∞,∞){displaystyle xin (-infty ,infty )}PDF Γ(ν+12)νπΓ(ν2)(1+x2ν)−ν+12{displaystyle extstyle {frac {Gamma left({frac { u +1}{2}} ight)}{{sqrt { u pi }},Gamma left({frac { u }{2}} ight)}}left(1+{frac {x{2}}{ u }} ight){-{frac { u +1}{2}}}!}CDF12+xΓ(ν+12)×2F1(12,ν+12;32;−x2ν)πνΓ(ν2){displaystyle {egin{matrix}{frac {1}{2}}+xGamma left({frac { u +1}{2}} ight) imes \[0.5em]{frac {,_{2}F_{1}left({frac {1}{2}},{frac { u +1}{2}};{frac {3}{2}};-{frac {x{2}}{ u }} ight)}{{sqrt {pi u }},Gamma left({frac { u }{2}} ight)}}end{matrix}}}
where 2F1 is the hypergeometric functionMean 0 for ν>1{displaystyle u >1}, o...取得本站獨家住宿推薦 15%OFF 訂房優惠
T-Distribution Student's T
T-Distribution is statistics. How to run a t-test, how to read a t-distribution and how to find t-distribution values. Step by step articles & videos.