Maximum likelihood estimation for constrained parameters of multinomial distributions - Application to Zipf-Mandelbrot models

F. Izsak

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    Abstract

    A numerical maximum likelihood (ML) estimation procedure is developed for the constrained parameters of multinomial distributions. The main dif��?culty involved in computing the likelihood function is the precise and fast determination of the multinomial coef��?cients. For this the coef��?cients are rewritten into a telescopic product. The presented method is applied to the ML estimation of the Zipf–Mandelbrot (ZM) distribution, which provides a true model in many real-life cases. The examples discussed arise from ecological and medical observations. Based on the estimates, the hypothesis that the data is ZM distributed is tested using a chi-square test. The computer code of the presented procedure is available on request by the author.
    Original languageUndefined
    Article number10.1016/j.csda.2006.05.008
    Pages (from-to)1575-1583
    Number of pages9
    JournalComputational statistics & data analysis
    Volume51
    Issue numbersuppl 2/3
    DOIs
    Publication statusPublished - 1 Dec 2006

    Keywords

    • EWI-8535
    • IR-66721
    • METIS-237780

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