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

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• 作者：C. Satheesh Kumar (1)
  A. Riyaz (1)
  
  1. Department of Statistics ; University of Kerala ; Trivandrum聽 ; 695 581 ; India
  
• 关键词：Cluster negative binomial distribution ; Generalized likelihood ratio test ; Logarithmic series distribution ; Maximum likelihood estimation ; Probability generating function
• 刊名：AStA Advances in Statistical Analysis
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：99
• 期：1
• 页码：31-43
• 全文大小：195 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Econometrics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1863-818X

文摘

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.