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[01452] Some Statistical Properties and Maximum Likelihood Estimation of Parameters of Bivariate Modified Weibull Distribution with its Real-Life Applications

  • Session Time & Room : 3E (Aug.23, 17:40-19:20) @E504
  • Type : Contributed Talk
  • Abstract : Real-life data sets with ties arise quite commonly in medicine, industry, reliability and survival analysis. We attempt to model such types of data sets using bivariate distributions with singular components. For this purpose, we consider mainly two types of approaches, namely the "Minimization approach" and the "Maximization approach." Using the minimization approach the bivariate modified Weibull (BMW) distribution is derived. Due to five parameters, the BMW is a more general and flexible distribution. It reduces to the Marshall-Olkin bivariate exponential (MOBE) and Marshall-Olkin bivariate Weibull (MOBW) distributions under certain parameter restrictions. Some distributional, modal and aging properties of BMW will be discussed. The copula associated with BMW distribution is given. Finally, we will discuss the maximum likelihood estimation of parameters of BMW distribution via the EM algorithm. We will give some numerical results of a real-life data set with ties.
  • Classification : 62Nxx, Mainly to developed models to analyze real life bivariate data sets where the ties occur naturally in the data sets. The data may be censored . Such type of models are known as Bivariate distributions with singular component.
  • Format : Talk at Waseda University
  • Author(s) :
    • Sanjay Kumar (Ph.D. Student, Department of Mathematics & Statistics, Indian Institute of Technology Kanpur)
    • Debasis Kundu (Professor, Department of Mathematics & Statistics, Indian Institute of Technology Kanpur)
    • Sharmishtha Mitra (Professor, Department of Mathematics & Statistics, Indian Institute of Technology Kanpur)