4.3.1—Fitted distributions

Fit a probability model by estimating its parameters from data, then compare expected behaviour with observed frequencies or summary features. A fitted model is an approximation, not an explanation by itself.

Keep class intervals consistent, calculate expected counts from model probabilities, and check that expected counts are large enough for the chosen test. Parameters estimated from the same data affect degrees of freedom.

Fit a Poisson model using the sample mean λ̂, then calculate each class probability from λ̂ before forming expected counts.

Matching the mean does not guarantee a good fit; dispersion, tail behaviour and the test statistic still matter.