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Author: Pavitra Kumari × End date: 2023 × Start date: 2023 × Thesis Type: Ph.D ×
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    ThesisItemOpen Access
    Bayesian Estimation for Some Lifetime Models under Different Loss Functions
    (Chaudhary Charan Singh Haryana Agricultural University hisar, 2023-01) Pavitra Kumari; Vinay Kumar
    The life testing experiments are carried out to obtain the lifetime data on patients for survival analysis and to study the reliability of electrical, electronic and mechanical systems, information theory, artificial intelligence, etc. This thesis deals with the classical and Bayesian estimation methods for the generalized of lifetime models. We consider four distinct loss functions, namely, square error loss function, entropy loss function, precautionary loss function, Linex loss function and type II censoring in this thesis. Type II censoring has the significant advantage that you know in advance how many failure times your test will yield. Generalizations of univariate lifetime distributions are often of interest to serve for real life phenomena. These generalized lifetime distributions are very useful in many fields such as medicine, physics, engineering and biology. We consider three distinct lifetime models, namely, Lomax, Rayleigh Lomax and IPBH lifetime model and developed statistical inferences for the associated model parameters and reliability characteristics from both the classical and Bayesian estimation perspectives in Chapter 4. Lomax distribution is one of the well-known univariate distributions that is considered as an alternative to the exponential, gamma and Weibull distributions for heavy tailed data. In this thesis, we introduce a generalization of the Lomax distribution called Rayleigh Lomax (RL) distribution. This distribution provides great fit in modelling wide range of real data sets. It is a very flexible distribution that is related to some of the useful univariate distributions such as exponential, Weibull and Rayleigh distributions. Moreover, this distribution can also be transformed to a lifetime distribution which is applicable in many situations. For example, we obtain the inverse estimation and confidence intervals. In present study apply AIC and BIC to detect the changes in parameters of the RL distribution. The performance of these approaches is studied through simulations and applications to real data sets. The statistical software R is used for computation throughout the thesis. Finally, a complete list of references and other literature surveys are given at the end of the thesis as a bibliography.