Student's t distribution | t distribution and gamma distribution
byMarcoTaboga[1],PhD TheStudentstdistributionisacontinuousprobabilitydistributionthatis oftenencounteredinstatistics(e.g.,in hypothesistestsaboutthemean[2]). ItariseswhenanormalrandomvariableisdividedbyaChi-squareoraGamma randomvariable. Howitarises Beforegoingintodetails,weprovideanoverview. Thestandardcase Avariable hasastandardStudentstdistributionwith degreesoffreedomifitcanbewrittenasaratio where: AChi-squareva...
The Students t distribution is a continuous probability distribution that is often encountered in statistics (e.g., in hypothesis tests about the mean[2]).
It arises when a normal random variable is divided by a Chi-square or a Gamma random variable.
How it arisesBefore going into details, we provide an overview.
The standard caseA variable has a standard Students t distribution with degrees of freedom if it can be written as a ratio
where:
A Chi-square variable with degrees of freedom divided by has a Gamma distribution[3] (with parameters and ).
As a consequence, we can also see a standard Students t distribution with degrees of freedom as a ra...