Bayesian Estimation Distribution and Survival Function of Records and Inter-Record Times and Numerical Computation for Weibull Model

Mahmoud Afshari

Abstract

In this paper, we consider an experiment from a sample whose size is determined by the values smaller than all previous ones which is record values. We suppose that the data available are lower record values such as L1, K1, L2, K2,..., Lr, Kr,..., where L1, L2,... are successive and K1,K2, ... are the numbers of trials needed to obtain new records. Bayesian estimation and survival function are obtained based on record values under square error and linear exponential loss functions or briefly (SEL, LLF). We consider weibull distribution with unknown two parameters \alpha and \beta. Estimation of both parameters and numerical computations under square error loss function are investigated.