In classical statistics, the parameter of interest θ is fix and estimated by the estimator \delta using some methods such as maximum likelihood method. In Bayesian framework, the parameter of interest θ is a random variable and then we can consider a density for it as \pi(\theta) which is prior distribution. The posterior distribution θ given data, \pi(\theta|data), is obtained by combining the likelihood function and the prior distribution. In this approach the loss function L(\theta,\delta)\ is important. The Bayesian estimator can be calculated by minimizing the posterior loss. Recently E-Bayesian estimation is proposed for estimation of the parameter which is the expectation of the Bayesian estimation over the hyperparameters of the prior distribution. In a sequence of observations, an upper record value is a value that is greater all values before. In this thesis, we consider record data and estimate the parameter of interest in geometric and exponential distributions based on record data, for further information, see Arnold et. al. (1998).
