Noncentral t | t distribution and gamma distribution
ProbabilitydistributionNoncentralStudentstProbabilitydensityfunctionParametersν>0degreesoffreedomμ∈ℜ{displaystylemuinRe,!}noncentralityparameterSupportx∈(−∞;+∞){displaystylexin(-infty;+infty),!}PDFseetextCDFseetextMeanseetextModeseetextVarianceseetextSkewnessseetextEx.kurtosisseetextThenoncentralt-distributiongeneralizesStudentst-distributionusinganoncentralityparameter.Whereasthecentralprobabilitydistributiondescribeshowateststatistictisdistributedwhenthedifferencetestedisnull,thenoncent...
Probability distribution
Noncentral Students tProbability density function
Parameters ν > 0 degrees of freedomμ∈ℜ{displaystyle mu in Re ,!} noncentrality parameterSupport x∈(−∞;+∞){displaystyle xin (-infty ;+infty ),!}PDF see textCDF see textMean see textMode see textVariance see textSkewness see textEx. kurtosis see textThe noncentral t-distribution generalizes Students t-distribution using a noncentrality parameter. Whereas the central probability distribution describes how a test statistic t is distributed when the difference tested is null, the noncentral distribution describes how t is distributed when the null is false. This leads to its use in statistics, especially calculating statistical power. The noncentral t-distribution is also known as the singly noncentral t-distribution, and in addition to its primary use in statistical inference, is also used in robust modeling for data.
Characterization[edit]If Z is a normally distributed ra...