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A zero-inflated logarithmic series distribution of order k and its applications

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  • C. Satheesh Kumar
  • A. Riyaz

Abstract

Here we develop an order k version of the zero-inflated logarithmic series distribution of Kumar and Riyaz [Staistica (accepted for publication), 2013b ] through its probability generating function, and derive an expression for its probability mass function. Certain recurrence relation for its probabilities, raw moments and factorial moments are also obtained, and the maximum likelihood estimation of its parameters is discussed. We have tested the significance of the additional parameters of the distribution by generalized likelihood ratio test and illustrated all these procedures using certain real-life data sets. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • C. Satheesh Kumar & A. Riyaz, 2015. "A zero-inflated logarithmic series distribution of order k and its applications," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 31-43, January.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:1:p:31-43
    DOI: 10.1007/s10182-014-0229-1
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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. 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.
    3. Xekalaki, Evdokia & Panaretos, John, 1989. "On Some Distributions Arising in Inverse Cluster Sampling," MPRA Paper 6252, University Library of Munich, Germany.
    4. Kumar C. Satheesh, 2010. "Binomial Poisson Distribution Revisited," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 183-188, January.
    5. C. Satheesh Kumar, 2009. "Some properties of kemp family of distributions," Statistica, Department of Statistics, University of Bologna, vol. 69(4), pages 311-316.
    6. 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.
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