2018
DOI: 10.1590/0001-3765201820170733
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Abstract: A new discrete distribution is introduced. The distribution involves the negative binomial and size biased negative binomial distributions as sub-models among others and it is a weighted version of the two parameter discrete Lindley distribution. The distribution has various interesting properties, such as bathtub shape hazard function along with increasing/decreasing hazard rate, positive skewness, symmetric behavior, and over-and under-dispersion. Moreover, it is self decomposable and infinitely divisible, w… Show more

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Cited by 8 publications
(4 citation statements)
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“…The WCG stems from the family of discrete models that uses a weighted function of a standard discrete-valued probability model [9] , [8] , [10] , [7] , [13] , [34] , [35] , [36] and is expressed as: 1 2 3 provided that exists. Here, is the Geometric probability function, that is, , where and .…”
Section: The Wcg Model and The Associated Inar-wcg Processmentioning
confidence: 99%
“…The WCG stems from the family of discrete models that uses a weighted function of a standard discrete-valued probability model [9] , [8] , [10] , [7] , [13] , [34] , [35] , [36] and is expressed as: 1 2 3 provided that exists. Here, is the Geometric probability function, that is, , where and .…”
Section: The Wcg Model and The Associated Inar-wcg Processmentioning
confidence: 99%
“…These techniques aim to create flexible distributions by the use of a tuning weight function and a well-established (simple) baseline distribution. For further details, we may refer the reader to Patil and Rao [13,14] for the general formalism with discussions, Castillo and Casany [6] for the Poisson distribution as a baseline, Bhati and Joshi [4] for the geometric distribution as a baseline and Bakouch [3] for the negative binomial Lindley distribution as a baseline, and the references therein. The mathematical backgrounds of the discrete weighted distributions can be formulated as follows.…”
Section: Introductionmentioning
confidence: 99%
“…The negative binomial distribution (that may arise as a mixture model by using a gamma distribution for the continuous part) is undoubtedly the most popular alternative to model extra- variability. There is extensive literature regarding other discrete mixed distributions that can accommodate different levels of overdispersion, for example, the Poisson–Lindley [ 2 ], the Poisson–lognormal [ 3 ], the Poisson–inverse Gaussian [ 4 ], the negative binomial–Lindley [ 5 ], the Poisson–Janardan [ 6 ], the two-parameter Poisson–Lindley [ 7 ], the Poisson–Amarendra [ 8 ], the Poisson–Shanker [ 9 ], the Poisson–Sujatha [ 10 ], the quasi-Poisson–Lindley [ 11 ], the weighted negative binomial–Lindley [ 12 ] the Poisson-weighted Lindley [ 13 ], the binomial-discrete Lindley [ 14 ], and the two-parameter Poisson–Sujatha [ 15 ], among many others.…”
Section: Introductionmentioning
confidence: 99%