Working Paper Article Version 1 This version is not peer-reviewed

An Over and Underdispersed Biparametric Extension of the Waring Distribution

Version 1 : Received: 3 December 2020 / Approved: 4 December 2020 / Online: 4 December 2020 (12:00:25 CET)

A peer-reviewed article of this Preprint also exists.

Cueva-López, V.; Olmo-Jiménez, M.J.; Rodríguez-Avi, J. An Over and Underdispersed Biparametric Extension of the Waring Distribution. Mathematics 2021, 9, 170. Cueva-López, V.; Olmo-Jiménez, M.J.; Rodríguez-Avi, J. An Over and Underdispersed Biparametric Extension of the Waring Distribution. Mathematics 2021, 9, 170.

Journal reference: Mathematics 2021, 9, 170
DOI: 10.3390/math9020170

Abstract

A new discrete distribution for count data called extended biparametric Waring (EBW) distribution is developed. Its name is related to the fact that, in a specific configuration of its parameters, it can be seen as a biparametric version of the univariate generalized Waring (UGW) distribution, a well-known model for the variance decomposition into three components: randomness, liability and proneness. Unlike the UGW distribution, the EBW can model both overdispersed and underdispersed data sets. In fact, the EBW distribution is a particular case of a UWG distribution when its first parameter is positive; otherwise, it is a particular case of a Complex Triparametric Pearson (CTP) distribution. Hence, this new model inherits most of their properties and, moreover, it helps to solve the identification problem in the variance components of the UGW model. We compare the EBW with the UGW by a simulation study, but also with other over and underdispersed distributions through the Kullback-Leibler divergence. Additionally, we have carried out a simulation study in order to analyse the properties of the maximum likelihood parameter estimates. Finally, some application examples are included which show that the proposed model provides similar or even better results than other models, but with fewer parameters.

Subject Areas

count data distribution; goodness of fit; overdispersion; underdispersion

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