{"title":"An Extension of the Geometric Distribution with Properties and Applications","authors":"S. Chakraborty, S. Ong, Aniket Biswas","doi":"10.17713/ajs.v52i3.1487","DOIUrl":null,"url":null,"abstract":"A new parameter is introduced to extend the geometric distribution using Azzalini's method. Several important structural properties of the proposed two-parameter extended geometric distribution are investigated. Characterizations including for the geometric distribution, in terms of the proposed model, are established. Maximum likelihood estimation, method of moment estimation and relative frequency based estimation of the parameters are discussed in detail. The likelihood ratio test regarding relevance of the additional parameter is presented. Bayesian estimation of the parameters using STAN is also discussed. The proposed model is compared with some recently introduced two-parameter count models by analyzing two real-life datasets. The findings clearly indicate superiority of the proposed model over the rest.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"13 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Austrian Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17713/ajs.v52i3.1487","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
A new parameter is introduced to extend the geometric distribution using Azzalini's method. Several important structural properties of the proposed two-parameter extended geometric distribution are investigated. Characterizations including for the geometric distribution, in terms of the proposed model, are established. Maximum likelihood estimation, method of moment estimation and relative frequency based estimation of the parameters are discussed in detail. The likelihood ratio test regarding relevance of the additional parameter is presented. Bayesian estimation of the parameters using STAN is also discussed. The proposed model is compared with some recently introduced two-parameter count models by analyzing two real-life datasets. The findings clearly indicate superiority of the proposed model over the rest.
期刊介绍：
The Austrian Journal of Statistics is an open-access journal (without any fees) with a long history and is published approximately quarterly by the Austrian Statistical Society. Its general objective is to promote and extend the use of statistical methods in all kind of theoretical and applied disciplines. The Austrian Journal of Statistics is indexed in many data bases, such as Scopus (by Elsevier), Web of Science - ESCI by Clarivate Analytics (formely Thompson & Reuters), DOAJ, Scimago, and many more. The current estimated impact factor (via Publish or Perish) is 0.775, see HERE, or even more indices HERE. Austrian Journal of Statistics ISNN number is 1026597X Original papers and review articles in English will be published in the Austrian Journal of Statistics if judged consistently with these general aims. All papers will be refereed. Special topics sections will appear from time to time. Each section will have as a theme a specialized area of statistical application, theory, or methodology. Technical notes or problems for considerations under Shorter Communications are also invited. A special section is reserved for book reviews.
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