{"title":"A Generalized Gompertz Distribution with Hazard Power Parameter and Its Bivariate Extension: Properties and Applications","authors":"Hiba Zeyada Muhammed","doi":"10.1007/s40745-022-00420-w","DOIUrl":null,"url":null,"abstract":"<div><p>Recently, a new class of distributions, named bivariate hazard power parameter family of distributions is introduced. In this paper, a generalized Gompertz distribution is introduced as a member of this family in both univariate and bivariate cases. Different properties are discussed as moments and moment generating function. It is observed that the joint probability density function and the joint survival function can be expressed in explicit forms. Maximum likelihood estimation is considered for the model unknown parameters. Asymptotic confidence intervals for the unknown parameters are evaluated. Some simulations have been performed to see the performances of the MLEs. Three real data sets are applied to this model for illustrative purposes.</p></div>","PeriodicalId":36280,"journal":{"name":"Annals of Data Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Data Science","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40745-022-00420-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Decision Sciences","Score":null,"Total":0}
引用次数: 0
Abstract
Recently, a new class of distributions, named bivariate hazard power parameter family of distributions is introduced. In this paper, a generalized Gompertz distribution is introduced as a member of this family in both univariate and bivariate cases. Different properties are discussed as moments and moment generating function. It is observed that the joint probability density function and the joint survival function can be expressed in explicit forms. Maximum likelihood estimation is considered for the model unknown parameters. Asymptotic confidence intervals for the unknown parameters are evaluated. Some simulations have been performed to see the performances of the MLEs. Three real data sets are applied to this model for illustrative purposes.
期刊介绍：
Annals of Data Science (ADS) publishes cutting-edge research findings, experimental results and case studies of data science. Although Data Science is regarded as an interdisciplinary field of using mathematics, statistics, databases, data mining, high-performance computing, knowledge management and virtualization to discover knowledge from Big Data, it should have its own scientific contents, such as axioms, laws and rules, which are fundamentally important for experts in different fields to explore their own interests from Big Data. ADS encourages contributors to address such challenging problems at this exchange platform. At present, how to discover knowledge from heterogeneous data under Big Data environment needs to be addressed. ADS is a series of volumes edited by either the editorial office or guest editors. Guest editors will be responsible for call-for-papers and the review process for high-quality contributions in their volumes.
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