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Distribution fit (MLE + KS)

Distribution fitting estimates a chosen family by maximum likelihood — normal, log-normal, gamma, Weibull, exponential or Poisson — with AIC/BIC and a KS test against the fitted curve.

What is Distribution fit (MLE + KS)?

The fit maximizes the likelihood (closed-form where available). AIC/BIC let you compare candidate families on the same data — fit two or three and keep the lowest. The Kolmogorov-Smirnov test checks absolute adequacy, though with estimated parameters its p-value is conservative (Lilliefors effect).

The histogram + fitted-density overlay is the honest visual check: systematic misfit in the tails matters more than the KS p.

When should I use Distribution fit (MLE + KS)?

  • Choosing a parametric model for skewed lab values, waiting times, or failure data.
  • Feeding parameters into power calculations or simulations.
  • Checking whether a log-normal or gamma describes a biomarker better than a normal.

What data does it need?

One numeric column + a distribution family.

What does it report?

Parameter MLEs ± SE, log-likelihood, AIC, BIC, KS D + p, histogram with fitted density overlay.

What does it assume?

  • Independent identically distributed observations.
  • Positive-support families (log-normal, gamma, Weibull, exponential) require strictly positive data; Poisson requires counts.

How do I interpret the result?

Compare AIC across families rather than reading one KS p in isolation. ΔAIC > 10 = essentially no support for the worse family.

See also

References

  • Venables & Ripley (2002). Modern Applied Statistics with S.
  • Burnham & Anderson (2002). Model Selection and Multimodel Inference.