= Noncentral t-distribution
{title2=$t_\nu(\delta)$}
{wiki}
If $Z\sim N(0,1)$ and $U\sim\chi^2_\nu$ are <independent>, then $(Z+\delta)/\sqrt{U/\nu}$ has the <noncentral t-distribution> with $\nu>0$ <statistical degrees of freedom> and noncentrality $\delta$. It describes the <test statistic> of a <Student's t-test> under a shifted <alternative hypothesis>. At $\delta=0$ it reduces to the <Student's t-distribution>. This is different from adding a constant to a central <Student t-distribution>: here the shift is inside the random denominator. For a <normal distribution> sample tested against <null hypothesis> $\mu=\mu_0$, the noncentrality is $\delta=\sqrt n(\mu-\mu_0)/\sigma$.
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