Measurement Scale and Upper Tail Sensitivity in Positive Data Model Comparison

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@article{1723687,
      author = {Okereke-Jude Esther Ogechi},
      title = {Measurement Scale and Upper Tail Sensitivity in Positive Data Model Comparison},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {10},
      number = {4},
      pages = {1246-1272},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1723687.pdf},
      abstract = {Background: A model that fits positive observations well may still give an unstable upper-tail estimate or depend on the numerical units used in fitting.
Methods: We examined eight established distributions using 24 mechanical-component failure times, 48 petroleum-rock measurements and 100 annual precipitation maxima. Maximum likelihood fitting used analytical profile reductions and checked numerical searches. Assessment combined corrected Akaike information criteria (AICc), empirical-distribution discrepancies, exact leave-one-out log scores and fitted upper quantiles. We also derived the scale properties of the unscaled inverse-power Burr–Hatke (IPBH) family and refitted it after controlled changes of numerical scale.
Results: Topp–Leone Burr–Hatke exponential had the lowest AICc and highest leave-one-out score in all three examples. For mechanical data, near-leading models gave 0.99 quantiles of 55.19 and 92.37 despite an AICc difference of about 0.31. The unscaled IPBH median always exceeds one, and its two shape parameters cannot absorb a nontrivial unit conversion. These restrictions explain its poor fit to the petroleum observations, all of which are below one. Profile refitting increased the precipitation IPBH log likelihood by 13.49 relative to the retained source solution.
Conclusions: Distribution comparisons should state the physical reference scale, check likelihood maximization and report the sensitivity of upper quantiles. The examples illustrate these issues; they do not independently validate predictions of rare extremes.},
      keywords = {inverse-power Burr–Hatke distribution; likelihood optimization; measurement scale; model comparison; upper quantiles},
      month = {October},
  }