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A Cautionary Note on Beta Families of Distributions and the Aliases Within

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  • Alan D. Hutson
  • Albert Vexler

Abstract

In this note, we examine the four parameter beta family of distributions in the context of the beta-normal and beta-logistic distributions. In the process, we highlight the concept of numerical and limiting alias distributions, which in turn relate to numerical instabilities in the numerical maximum likelihood fitting routines for these families of distributions. We conjecture that the numerical issues pertaining to fitting these multiparameter distributions may be more widespread than has originally been reported across several families of distributions.

Suggested Citation

  • Alan D. Hutson & Albert Vexler, 2018. "A Cautionary Note on Beta Families of Distributions and the Aliases Within," The American Statistician, Taylor & Francis Journals, vol. 72(2), pages 121-129, April.
    • Handle: RePEc:taf:amstat:v:72:y:2018:i:2:p:121-129
    DOI: 10.1080/00031305.2016.1213661
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    References listed on IDEAS

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    1. David A. Hennessy, 2009. "Crop Yield Skewness Under Law of the Minimum Technology," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(1), pages 197-208.
    2. Alan Hutson, 2004. "Utilizing the Flexibility of the Epsilon-Skew-Normal Distribution for Common Regression Problems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(6), pages 673-683.
    3. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    4. Jochen Ranger & Jörg-Tobias Kuhn, 2015. "Modeling Information Accumulation in Psychological Tests Using Item Response Times," Journal of Educational and Behavioral Statistics, , vol. 40(3), pages 274-306, June.
    5. Mameli, Valentina, 2015. "The Kumaraswamy skew-normal distribution," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 75-81.
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