Mathematics And Statistics - Research Publications

Permanent URI for this collectionhttps://kr.cup.edu.in/handle/32116/47

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Author: search.filters.author.Khetan, MuktiSubject: search.filters.subject.Weibull 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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    Modeling Bivariate Data Using Linear Exponential and Weibull Distributions as Marginals
    (De Gruyter Open Ltd, 2023-08-04T00:00:00) Arshad, Mohd; Pathak, Ashok Kumar; Azhad, Qazi J.; Khetan, Mukti
    Modeling bivariate data with different marginals is an important problem and have numerous applications in diverse disciplines. This paper introduces a new family of bivariate generalized linear exponential Weibull distribution having generalized linear and exponentiated Weibull distributions as marginals. Some important quantities like conditional distributions, conditional moments, product moments and bivariate quantile functions are derived. Concepts of reliability and measures of dependence are also discussed. The methods of maximum likelihood and Bayesian estimation are considered to estimate model parameters. Monte Carlo simulation experiments are performed to demonstrate the performance of the estimators. Finally, a real data application is also discussed to demonstrate the usefulness of the proposed distribution in real-life situations. � 2023 Mathematical Institute Slovak Academy of Sciences.