{"title":"Modi-Weibull Distribution: Inferential and Simulation Study","authors":"Harshita Kumawat, Kanak Modi, Pankaj Nagar","doi":"10.1007/s40745-023-00491-3","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents a study on a new family of distributions using the Weibull distribution and termed as Modi-Weibull distribution. This Modi-Weibull distribution is based on four parameters. To understand the behaviour of the distribution, some statistical characteristics have been derived, such as shapes of density and distribution function, hazard function, survival function, median, moments, order statistics etc. These parameters are estimated using classical maximum likelihood estimation method. Asymptotic confidence intervals for parameters of Modi-Weibull distribution are also obtained. A simulation study is carried out to investigate the bias, MSE of proposed maximum likelihood estimators along with coverage probability and average width of confidence intervals of parameters. Two applications to real data sets are discussed to illustrate the fitting of the proposed distribution and compared with some well-known distributions.</p></div>","PeriodicalId":36280,"journal":{"name":"Annals of Data Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40745-023-00491-3.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Data Science","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40745-023-00491-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Decision Sciences","Score":null,"Total":0}
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Abstract
This paper presents a study on a new family of distributions using the Weibull distribution and termed as Modi-Weibull distribution. This Modi-Weibull distribution is based on four parameters. To understand the behaviour of the distribution, some statistical characteristics have been derived, such as shapes of density and distribution function, hazard function, survival function, median, moments, order statistics etc. These parameters are estimated using classical maximum likelihood estimation method. Asymptotic confidence intervals for parameters of Modi-Weibull distribution are also obtained. A simulation study is carried out to investigate the bias, MSE of proposed maximum likelihood estimators along with coverage probability and average width of confidence intervals of parameters. Two applications to real data sets are discussed to illustrate the fitting of the proposed distribution and compared with some well-known distributions.
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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