Statistics/Distributions/Student-t

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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 .

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