Bayesian Inference using Record Values from Inverted Probability Distributions

Abstract

In real life the record values arise in a natural way, for example, records in sports, weather, temperatures, economic, etc. It is thus important to model those records with the help of probability distributions for prediction purposes. In this thesis, the parameters of the inverted Topp-Leone and inverted Gompertz distributions are estimated using upper and lower record values, respectively, with the help of maximum likelihood, Bayes and empirical Bayes methods of estimation.The Bayes and empirical Bayes estimators are developed under both symmetric and asymmetric loss functions using informative and non-informative priors. For the empirical Bayes estimators, the hyperparameters are estimated using the methods of moments and maximum likelihood. Moreover, the prediction intervals for the future upper and lower record values are also derived.