Department Of Mathematics And Statistics

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Subject: search.filters.subject.exponential distribution

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    A Novel Bivariate Generalized Weibull Distribution with Properties and Applications
    (Taylor and Francis Ltd., 2023-09-09T00:00:00) Pathak, Ashok Kumar; Arshad, Mohd; J. Azhad, Qazi; Khetan, Mukti; Pandey, Arvind
    Univariate Weibull distribution is a well known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose univariate marginals are exponentiated Weibull distribution. Different statistical quantiles like marginals, conditional distribution, conditional expectation, product moments, correlation and a measure component reliability are derived. Various measures of dependence and statistical properties along with aging properties are examined. Further, the copula associated with BGW distribution and its various important properties are also considered. The methods of maximum likelihood and Bayesian estimation are employed to estimate unknown parameters of the model. A Monte Carlo simulation and real data study are carried out to demonstrate the performance of the estimators and results have proven the effectiveness of the distribution in real-life situations. � 2023 Taylor & Francis Group, LLC.
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    Parameteric Estimation for Reliability Function of Phased Mission Systems with Series Network
    (World Scientific, 2022-12-20T00:00:00) Dewan, Isha; Jain, Kanchan; Kapoor, Harmanpreet Singh; Rani, Monika
    In this paper, we consider a phased mission system consisting of k phases (subsystems) wherein the control flows sequentially. The mission is successful if tasks associated with every phase are successful. Density and reliability functions of the lifetime of such a system are worked out when the lifetimes of components of the subsystems follow exponential distribution. It is assumed that components in different subsystems are in series configuration and function independently. The subsystems are assumed to operate independently. A simulation study is conducted to find bias of the estimates of the parameters and the reliability function. The Root Mean Square Error (RMSE) of the estimates is also calculated. � 2023 World Scientific Publishing Company.