- #1
mnb96
- 715
- 5
Hello,
it is well-known that the Chi-square test between an observed distribution O and an expected distribution E can be interpreted as a test based on (twice) the second order Taylor approximation of the Kullback-Leibler divergence, i.e.: [tex]2\,\mathcal{D}_{KL}(O \| E) \approx \sum_i \frac{(O_i-E_i)^2}{E_i} = \chi^2[/tex]
where i is the bin of the histogram (or contigency table). A proof is given here (page 5).
The question is: how do we know that each of the error terms [itex]\frac{(O_i-E_i)^2}{E_i}[/itex] on the right side of the above equation follows a normal distribution N(0,1)? There is probably some some assumption to be made...?
it is well-known that the Chi-square test between an observed distribution O and an expected distribution E can be interpreted as a test based on (twice) the second order Taylor approximation of the Kullback-Leibler divergence, i.e.: [tex]2\,\mathcal{D}_{KL}(O \| E) \approx \sum_i \frac{(O_i-E_i)^2}{E_i} = \chi^2[/tex]
where i is the bin of the histogram (or contigency table). A proof is given here (page 5).
The question is: how do we know that each of the error terms [itex]\frac{(O_i-E_i)^2}{E_i}[/itex] on the right side of the above equation follows a normal distribution N(0,1)? There is probably some some assumption to be made...?