An Over and Underdispersed Biparametric Extension of the Waring Distribution

Valentina Cueva-López, María José Olmo-Jiménez and José Rodríguez-Avi
Additional contact information
Valentina Cueva-López: Department of Statistics and Operations Research, University of Jaén, 23071 Jaén, Spain
María José Olmo-Jiménez: Department of Statistics and Operations Research, University of Jaén, 23071 Jaén, Spain
José Rodríguez-Avi: Department of Statistics and Operations Research, University of Jaén, 23071 Jaén, Spain

Mathematics, 2021, vol. 9, issue 2, 1-15

Abstract: A new discrete distribution for count data called extended biparametric Waring ( E B W ) 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 ( U G W ) distribution, a well-known model for the variance decomposition into three components: randomness, liability and proneness. Unlike the U G W distribution, the E B W can model both overdispersed and underdispersed data sets. In fact, the E B W distribution is a particular case of a U W G distribution when its first parameter is positive; otherwise, it is a particular case of a Complex Triparametric Pearson ( C T P ) 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 U G W model. We compare the E B W with the U G W 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.

Keywords: count data distribution; goodness of fit; overdispersion; underdispersion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/2/170/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/2/170/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:2:p:170-:d:480886

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().