Poisson-Weighted Exponential Univariate Version and Regression Model With Applications

Abstract

This study introduces a new two-parameter mixed Poisson distribution, namely Poisson-Weighted Exponential (P-WE), which is obtained by mixing Poisson distribution with a new class of weighted exponential distribution. The new P-WE distribution provides a more flexible alternative for modelling over dispersed count data compared to Poisson distribution. The estimation procedures of P-WE distribution via method of moments and maximum likelihood are provided. This study also introduces P-WE regression model which can be fitted to over dispersed count data with covariates. The P-WE distribution and P-WE regression model are fitted to two sets of count data.

Exploring the application of the Negative Binomial–Generalized Exponential model for analyzing traffic crash data with excess zeros

“…To overcome this problem, researchers have proposed different tools for analyzing datasets with a large number of zeros and long tails. They include the zero-inflated (ZI) models (Shankar et al, 1997;Shankar et al, 2003), the Negative Binomial-Lindley (NB-L) model (Geedipally et al, 2012;Hallmark et al, 2013;Xu and Sun, 2015), the Poisson-weighted exponential model (Zamani et al, 2014), the Poisson Inverse Gaussian (PIG) (Zha et al, 2015), the Negative Binomial-Crack (NB-CR) distribution (Saengthong and Bodhisuwan, 2013), and the Sichel (SI) model (Zou et al, 2013;2015). Lord et al (2005Lord et al ( , 2007 and Lord and Geedipally (2011; provide discussions about the advantages and limitations of these distributions and models.…”

Modeling and Forecasting of International Tourism Demand in ASEAN Countries

“…Several parameterizations were performed for the generalized Poisson and negative binomial regression models (Famoye et al, 2004;Wang and Famoye, 1997;Zamani and Ismail, 2012;Greene, 2008;Zamani et al, 2014). One of the parameterization of the GP regression model, which is used in this study, was used by Wang and Famoye (1997) for analyzing household fertility count data and by Ismail and Jemain (2007) for analyzing the Malaysian claim count data.…”

A new model for over-dispersed count data: Poisson quasi-Lindley regression model

“…x ik is the vector of covariates and = 0 , 1 , 2 , … k T is the unknown vector of regression coefficients. Inserting (16) in (5), the log-likelihood function can be obtained as follows where = ( , ) T . The unknown parameters, and = 0 , 1 , 2 , … k T , are obtained by maximizing (16) with the nlm function of R software.…”

“…The reason for that comes from its simple form and easy implementation and software support. To remove the drawback of Poisson distribution, researchers have shown great interest to introduce mixed-Poisson distributions for modeling the over-dispersed or under-dispersed count data sets such as Bhati et al [1], Imoto et al [7], Mahmoudi and Zakerzadeh [9], Gencturk and Yigiter [5], Wongrin and Bodhisuwan [15], Déniz [3], Cheng et al [2], Lord and Geedipally [8], Zamani et al [16], Sáez-Castillo and Conde-Sánchez [12], Rodríguez-Avi et al [10], Shmueli et al [11], Shoukri et al [13].…”