الفهرس 
Some Non-Bayesian Techniques of EstimationOnly 14 pages are availabe for public view
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Abstract
Surles and Padgett (2001) proposed the generalized Rayleigh distribution, which is widely used for modeling and analyzing skewed data in various fields, including medicine, engineering, and the life sciences. This thesis aims to accomplish two primary objectives.
The first objective focuses on estimating the unknown scale and shape parameters of the generalized Rayleigh distribution using trimmed samples. This is achieved through both maximum likelihood estimation and the Bayesian framework. Bayesian analysis of the parameters is obtained using different approaches, including a linear exponential loss function, a noninformative prior, a general entropy loss function, and an informative prior. The performance of maximum likelihood estimation and Bayesian estimators is compared using Markov Chain simulation. Simulation techniques are employed to evaluate the efficacy of various estimation techniques. Additionally, real data on the duration of remission (in months) for a random sample of bladder cancer patients are used to demonstrate the suggested inference methods and determine the effectiveness of the linear exponential loss function in real-life scenarios. All calculations and numerical results are performed using Mathcad (version 14) for Statistical Computing.
The second objective involves estimating an unknown shape parameter for the generalized Rayleigh distribution using maximum likelihood, Bayesian, and expected Bayesian estimation techniques under a type-II censoring scheme. Subsequently, the estimators of Bayesian and expected Bayesian are evaluated using four different loss functions: the linear exponential loss function, the weighted linear exponential loss function, the compound linear exponential loss function, and the weighted compound linear exponential loss function that is a novel suggested loss function generated by combining weights with the compound linear exponential loss function. We use gamma distribution within the Bayesian framework as a prior distribution. Additionally, the expected Bayesian estimator is obtained through three prior distributions of the hyperparameters.
Moreover, depending on the four distinct forms of loss functions, expected Bayesian and Bayesian estimation techniques are performed using Monto Carlo simulations to verify the effectiveness of the suggested loss function and to compare maximum likelihood estimation, Bayesian, and expected Bayesian estimation techniques. Furthermore, the simulation results indicate that, depending on the minimum mean squared error, the Bayesian and expected Bayesian estimations corresponding to the weighted compound linear exponential loss function suggested in this paper have significantly better performance compared to other loss functions, and the expected Bayesian estimator also performs better than the Bayesian estimator. Finally, the proposed inference techniques are demonstrated using a set of actual data from the medical field to clarify the applicability of the suggested estimators to real phenomena. Also, shows that the discussed weighted compound linear exponential loss function is efficient and can be applied in a real-life scenario. All calculations and numerical results have been done using the R-Statistical Programming Language for Statistical Computing.