Goodness of Fit Test

Used to check whether a set of observed categorical data follows a theoretical distribution such as uniform or Poisson.

Hypotheses

$H_0 : \text{Data follow the specified distribution.}$

$H_1 : \text{Data do not follow the specified distribution.}$

Degrees of freedom

$$\nu = k - p - 1$$

Here:

• $k$: number of non-empty classes
• $p$: number of estimated parameters

Test Statistic

$$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \quad \sim \chi^2_\nu$$