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, which makes the proposed distribution well suited for count data modeling. Other properties are investigated, including probability generating function, ordinary moments, factorial moments, negative moments and characterization. Estimation of the model parameters is investigated by the methods of moments and maximum likelihood, and a performance of the estimators is assessed by a simulation study. The credibility of the proposed distribution over the negative binomial, Poisson and generalized Poisson distributions is discussed based on some test statistics and four real data sets.
Highlights
In observational studies it is observed that due to lack of well defined sampling frames for plant, human, insect, wildlife and fish populations, the scientists/ researchers cannot select sampling units with equal probability
Estimation of parameters of the distribution is investigated by the methods of moments (MM) and maximum likelihood (ML), and a performance of the estimators is assessed by a simulation study
Let Y1,Y2, . . . ,Yn be a random sample drawn from the weighted negative binomial Lindley (WNBL) distribution with the observed values x1, x2, . . . , xn
Summary
In observational studies it is observed that due to lack of well defined sampling frames for plant, human, insect, wildlife and fish populations, the scientists/ researchers cannot select sampling units with equal probability. The section ’Statistical Properties Of The WNBL Distribution’ gives several properties of the proposed distribution, such as probability generating function, moments, factorial moments, recurrence relation between moments and negative moments. The proposed model overcomes the heterogeneity issue and handles the over-dispersion because of its mixture representation which makes it better than the negative binomial, Poisson and generalized Poisson distributions. In view of the discussion above, some other motivational factors of the proposed model shall be outlined later and they are: i) Possessing BTS hazard function along with increasing/decreasing hazard rate characteristics which are seldom observed in discrete distributions. Corollary 1: In equation (6), if t is replaced by et, we get the moment generating function (mgf) of the WNBL distribution as MY (1 + pet (β 2 − 1))qβ+1 + p(β 2 − 1))(1 − pet )β+1. Estimation of parameters of the distribution is investigated by the methods of moments (MM) and maximum likelihood (ML), and a performance of the estimators is assessed by a simulation study
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
