Noncentral t-distribution

Noncentral Student's t
Probability density function
Parameters	ν > 0 degrees of freedom ${\displaystyle \mu \in \Re \,\!}$ noncentrality parameter
Support	${\displaystyle x\in (-\infty$ ;+\infty )\,\!}
PDF	see text
CDF	see text
Mean	see text
Mode	see text
Variance	see text
Skewness	see text
Excess kurtosis	see text

The noncentral t-distribution generalizes Student's 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.