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An order version of the alternative zero-inflated logarithmic series distribution and its applications

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  • C. Satheesh Kumar
  • A. Riyaz

Abstract

Here we introduce an order $ k $ k version of the alternative zero-inflated logarithmic series distribution of Kumar and Riyaz [14] and investigate some of its important properties by deriving an expression for its probability mass function, recurrence relations for its probabilities, raw moments and factorial moments. We discuss the estimation of the parameters of the distribution by the method of maximum likelihood. Certain test procedures are developed for testing the significance of the additional parameters of the model. All these procedures discussed in the paper are illustrated with the help of real life data sets. A simulation study is also considered for assessing the performance of the estimators.

Suggested Citation

  • C. Satheesh Kumar & A. Riyaz, 2016. "An order version of the alternative zero-inflated logarithmic series distribution and its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2681-2695, October.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:14:p:2681-2695
    DOI: 10.1080/02664763.2016.1142949
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    References listed on IDEAS

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    1. Panaretos, John & Xekalaki, Evdokia, 1986. "On Some Distributions Arising from Certain Generalized Sampling Schemes," MPRA Paper 6249, University Library of Munich, Germany.
    2. Puig, Pedro, 2003. "Characterizing Additively Closed Discrete Models by a Property of Their Maximum Likelihood Estimators, With an Application to Generalized Hermite Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 687-692, January.
    3. C. Satheesh Kumar & A. Riyaz Riyaz, 2013. "On zero - inflated logarithmic series distribution and its modification," Statistica, Department of Statistics, University of Bologna, vol. 73(4), pages 477-492.
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