List of formulas and concepts related to the hypothesis about the type of distribution:
- Null Hypothesis (H0): The assumption that the data follows a particular distribution (e.g. normal, exponential, etc.).
- Alternative Hypothesis (H1): The proposition that the data does not follow the expected distribution.
- Goodness-of-fit criterion (for example, the Kolmogorov-Smirnov criterion):
- ( D = \max |F_n(x) – F(x)| )
- where ( F_n(x) ) is the empirical distribution function, and ( F(x) ) is the theoretical distribution function.
- Chi-square test:
- ( \chi^2 = \sum \frac{(O_i – E_i)^2}{E_i} )
- where ( O_i ) are the observed frequencies, ( E_i ) are the expected frequencies.
- Shapiro-Wilk test: Used to test the normality of distribution.
- Test statistics: ( W = \frac{(b^2)}{(a^2)} )
- where (a) and (b) are sample-dependent parameters.
- Anderson-Darling test: An alternative to the Kolmogorov-Smirnov test that is more sensitive to the tails of the distribution.
- Mann-Whitney test: Used to test the hypothesis of equality of distributions of two samples.