{"title":"The extended Burr XII distribution: properties and applications","authors":"A. Afify, Ashraf D. Abdellatif","doi":"10.22436/jnsa.013.03.02","DOIUrl":null,"url":null,"abstract":"This paper introduces a new four-parameter lifetime model called the Marshall-Olkin generalized Burr XII (MOGBXII) distribution. We derive some of its mathematical properties, including quantile and generating functions, ordinary and incomplete moments, mean residual life, and mean waiting time and order statistics. The MOGBXII density can be expressed as a linear mixture of Burr XII densities. The maximum likelihood and least squares methods are used to estimate the MOGBXII parameters. Simulation results are obtained to compare the performances of the two estimation methods for both small and large samples. We empirically illustrate the flexibility and importance of the MOGBXII distribution in modeling various types of lifetime data.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/jnsa.013.03.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
This paper introduces a new four-parameter lifetime model called the Marshall-Olkin generalized Burr XII (MOGBXII) distribution. We derive some of its mathematical properties, including quantile and generating functions, ordinary and incomplete moments, mean residual life, and mean waiting time and order statistics. The MOGBXII density can be expressed as a linear mixture of Burr XII densities. The maximum likelihood and least squares methods are used to estimate the MOGBXII parameters. Simulation results are obtained to compare the performances of the two estimation methods for both small and large samples. We empirically illustrate the flexibility and importance of the MOGBXII distribution in modeling various types of lifetime data.
本文介绍了一种新的四参数寿命模型Marshall-Olkin广义Burr XII (MOGBXII)分布。我们得到了它的一些数学性质，包括分位数和生成函数、普通矩和不完全矩、平均剩余寿命、平均等待时间和序统计量。MOGBXII密度可以表示为Burr XII密度的线性混合物。使用极大似然和最小二乘法估计MOGBXII参数。仿真结果比较了两种估计方法在小样本和大样本情况下的性能。我们通过经验说明了MOGBXII分布在建模各种类型的生命周期数据中的灵活性和重要性。
期刊介绍：
The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.
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