Bivariate alpha-generalized hyper-Poisson distribution: Properties and applications. (2nd April 2016)

• Record Type: Journal Article
• Authors: Satheesh Kumar, C.; Unnikrishnan Nair, B.
• Is Part Of: Journal of statistical theory and practice. Volume 10:Number 2(2016)
• Page Start: 405
• Page End: 419
• Publication Date: 2016-04-02
• Subjects: Confluent hypergeometric function -- displaced Poisson distribution -- factorial moment generating function -- Hermite distribution -- Poisson distribution; Primary 60E05 -- 60E10 -- Secondary 33C20; 519.505
• DOI: 10.1080/15598608.2016.1156039
• Languages: English
• ISSNs: 1559-8608

Abstract

ABSTRACT: A bivariate version of the alpha-generalized hyper-Poisson distribution of Kumar and Nair is considered here through its probability generating function and is studied in terms of some of its important aspects by deriving its probability mass function, factorial moments, and marginal and conditional distributions and obtaining certain recursion formulas for its probabilities, raw moments, and factorial moments. The method of maximum likelihood is applied for estimating the parameters of the distribution, and the generalized likelihood ratio test is considered for testing the significance of its additional parameter. All these procedures are illustrated with the help of two real-life data sets, and a simulation study is conducted for assessing the performance of the estimators obtained by the maximum likelihood estimation method.