Statistics/Distributions/Student-t

Student-t Distribution
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:

$$ t = \frac{\mbox{Z}}{ \sqrt{ \chi_{r}^2 /r }} $$

where $$ Z = \frac{X - \bar{X}}{\sigma} $$ and $$ \chi_{r}^2 = \chi_{r_1}^2 + ... + \chi_{r_n}^2 $$.