{"title":"一个柔性浴盆形失效时间模型的性质及相关推断","authors":"N. Choudhary, Abhishek Tyagi, B. Singh","doi":"10.6092/ISSN.1973-2201/10025","DOIUrl":null,"url":null,"abstract":"In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.","PeriodicalId":45117,"journal":{"name":"Statistica","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference\",\"authors\":\"N. Choudhary, Abhishek Tyagi, B. Singh\",\"doi\":\"10.6092/ISSN.1973-2201/10025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.\",\"PeriodicalId\":45117,\"journal\":{\"name\":\"Statistica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2021-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.6092/ISSN.1973-2201/10025\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6092/ISSN.1973-2201/10025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
摘要
在本研究中,我们引入了一个带有额外形状参数的修正威布尔分布的扩展版本,以便为其密度和危险率函数提供更大的灵活性。该分布能够模拟出浴缸型、递减型、递增型和恒定型的危险率函数。该模型包含了在生命周期数据分析中广泛使用的子模型,如修正Weibull、Chen、极值、Weibull、Rayleigh和指数分布。我们研究了它的统计性质,包括危险率函数、矩和阶统计量的分布。采用极大似然法和贝叶斯估计法对模型中涉及的参数进行估计。在贝叶斯估计中,我们假设参数具有独立的Gamma先验,并采用Gibbs采样器中的Metropolis-Hastings算法等MCMC技术来获得基于样本的估计量和参数的最高后验密度区间。Tierney and Kadane(1986)近似也用于获得参数的贝叶斯估计。为了突出所获得的各种估计的相对重要性,进行了模拟研究。用两个实际数据集说明了该模型的有效性。
A Flexible Bathtub-Shaped Failure Time Model: Properties and Associated Inference
In this study, we introduce an extended version of the modified Weibull distribution with an additional shape parameter, in order to provide more flexibility to its density and the hazard rate function. The distribution is capable of modeling the bathtub-shaped, decreasing, increasing and the constant hazard rate function. The proposed model contains sub-models that are widely used in lifetime data analysis such as the modified Weibull, Chen, extreme value, Weibull, Rayleigh, and exponential distributions. We study its statistical properties which include the hazard rate function, moments and distribution of the order statistics. The parameters involved in the model are estimated by using maximum likelihood and the Bayesian method of estimation. In Bayesian estimation, we assume independent Gamma priors for the parameters and MCMC technique such as the Metropolis-Hastings algorithm within Gibbs sampler has been implemented to obtain the sample-based estimators and the highest posterior density intervals of the parameters. Tierney and Kadane (1986) approximation is also used to obtain Bayes estimators of the parameters. In order to highlight the relative importance of various estimates obtained, a simulation study is carried out. The usefulness of the proposed model is illustrated using two real datasets.