الفهرس | Only 14 pages are availabe for public view |
Abstract In statistics, the problem of outliers is an important in almost all experimental fields. The existence of outliers in the data might distort the estimated model parameters as well as the model’s goodness of fit. Outliers deserve special consideration since even little deviations from the assumed model can have a severe influence on the efficiency of parameter estimates. In this thesis, the estimation of the entropy for the power function distribution in the presence of outliers and homogenous case is obtained using the methods of maximum likelihood and Bayesian estimations. The Markov Chain Monte Carlo method using Gibbs sampling is developed due to the lack of explicit forms for the Bayesian estimates. A simulation study is implemented to compute and compare the performance of estimates in both methods with respect to absolute biases and mean squared errors. Application to real data set is given to confirm the results of study. The estimation of entropy and extropy for Pareto distribution in the presence of outliers and homogenous case is discussed in this thesis. The maximum likelihood and Bayesian estimations using different loss functions are applied to estimate the entropy measure. Markov Chain Monte Carlo procedure using Metropolis-Hastings algorithm is used to generate posterior random variables. Monte Carlo procedure using simulations is designed to implement the precision of estimates for different sample sizes and number of outliers. The performance of estimates is planned by experiments with real data. Furthermore, estimating of stress-strength reliability model in the presence of outliers and homogenous case using the maximum likelihood and Bayesian methods is regarded. Bayesian estimators of = P(Y < X ) are derived by considering the independent gamma priors. A simulation study is implemented to compute and compare the performance of estimates. Also, application to real-data is also used. |