Docs

Understanding the goodness-of-fit tests

WhichDist ranks candidates with an AICc-led composite and always shows the classical tests so you can judge absolute fit, not just the relative order. Same info buttons appear next to each metric inside the add-in.

• AICc — corrected Akaike Information Criterion. Balances fit quality against the number of parameters, with a small-sample correction. Lower is better; it leads the ranking.
• AIC — rewards good fit, penalizes extra parameters. Lower is better; AICc is preferred for small samples.
• BIC — like AIC but penalizes parameters more strongly, so it favors simpler models. Lower is better.
• KS (Kolmogorov–Smirnov) — the largest gap between the empirical and fitted CDFs. Smaller = closer fit; most sensitive around the centre.
• AD (Anderson–Darling) — like KS but weights the tails more heavily, so it catches a poor fit in the extremes. Smaller is better.
• χ² (chi-squared) — compares observed vs. expected counts across bins (for discrete data). Smaller = closer agreement.

How to read the plots

• Histogram + PDF/PMF — bars are your data’s density; the curve is the fitted model. A good fit hugs the tops of the bars with no systematic gaps.
• ECDF vs CDF — dots are the empirical cumulative distribution; the line is the fitted CDF. A good fit keeps the dots on the curve across the whole range.
• Q–Q plot — fitted-theoretical quantiles vs. your sorted data. Points on the dashed y = x line mean a good fit; a systematic curve away from it reveals skew or heavy tails.
• Top-3 overlay — the three best-ranked PDFs over your histogram, so you can see how close the runners-up are to the winner.