A multimodal beta distribution with application to economic data

Volume 34 / 2007

Saralees Nadarajah, Samuel Kotz Applicationes Mathematicae 34 (2007), 1-14 MSC: 33C90, 62E99. DOI: 10.4064/am34-1-1


Beta distributions are popular models for economic data. In this paper, a new multimodal beta distribution with bathtub shaped failure rate function is introduced. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix. Finally, an application to consumer price indices is illustrated to show that the proposed distribution is a better model to economic data than one based on the standard beta distribution.


  • Saralees NadarajahSchool of Mathematics
    University of Manchester
    Manchester M60 1QD, UK
  • Samuel KotzDepartment of Engineering Management
    and Systems Engineering
    George Washington University
    Washington, DC 20052, U.S.A.

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