I think there are two ways to perform the chi-Square goodness-of-fit test:
- Divide the sample space into bins of equal size and see how many observed values fall in each bin. where the expected per bin depends on the fit.
- Divide the cdf of the fit into B bins of equal size (e.g., five bins of size .2 each, or 8 bins of width .125 each) and see where each observed value would belong into. -> count observed values per bin of size > calculate the chi square statistic (where the expected nr per bin is n/B or observations/bins, since the quantiles are distributed uniformly)
Is 2. a valid approach? And is there anything noteworthy about the second approach?