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  "Title": "Maxwell Boltzmann Bose Einstein Fermi Dirac Distribution and\nDestruction Rate Modelling",
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      "source": "Introduction.Rmd",
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      "title": "Exposure rating, destruction rate models and the mbbefd package",
      "author": "Christophe Dutang, Markus Gesmann, Giorgio Spedicato",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction and general notation",
        "Loss Distribution",
        "Expected Loss",
        "Limited Expected Loss",
        "Loss Cost of a Layer",
        "Increased Limit Factor",
        "Exposure curves",
        "Normalising loss experience using TIV and MPL",
        "Analysing deductibles",
        "Destruction rate models",
        "Classic distributions",
        "Uniform distribution",
        "Beta distribution",
        "One-inflated distributions",
        "Characterizations",
        "The one-inflated beta distribution",
        "The MBBEFD distribution, first parametrization",
        "Characterization by the exposure curve",
        "Distribution, density and quantile functions",
        "Moments",
        "The MBBEFD distribution, second parametrization",
        "Parameter domain",
        "Fitting methods and pricing examples",
        "Fitting methods: MLE and TLMME",
        "Examples",
        "Computation of premium rate (example)",
        "Losses below deductible",
        "Losses above deductible, but below limit",
        "Losses above limit",
        "Premium Rate",
        "References"
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      "created": "2026-01-19 22:08:25",
      "modified": "2026-01-27 16:51:04",
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