Statistics/Distributions/Student-t

Student t-distribution (or just t-distribution for short) is derived from the chi-square and normal distributions. We divide the standard normally distributed value of one variable over the root of a chi-square value over its r degrees of freedom. Mathematically, this appears as:

$t=\frac{\text{Z}}{\sqrt{{\chi }_r^2/r}}$

where $Z=\frac{X-\overline{X}}{\sigma }$ and ${\chi }_r^2={\chi }_{r_1}^2+...+{\chi }_{r_n}^2$.