Bayesian inference for exponential distribution based on upper record range

The aim of this paper is to obtain Bayesian estimations of scale parameter of the exponential distribution based on upper record range (Rn). We accomplish this purpose in two steps: point and interval. As the first step, the quadratic, squared error and absolute error, loss functions are considered for obtaining Bayesian-point estimations. Also in the next step, we find the shortest Bayes interval (hight posterior density interval) and Bayes interval with equal tails based on upper record range. Then, limits of Hight Posterior Density intervals are calculated by a so-called numerical method which is named homotopy perturbation methods. Moreover, we try to meet the admissibility conditions for linear estimators based on upper record range of the form mRn + d using the obtained Bayesian point estimations. With regard to the loss functions, the prior distribution between the conjunction family is chosen to be such as to be able to produce the linear estimations from upper record range statistics. Finally, some numerical examples and simulations are presented. [MediaObject not available: see fulltext.] © 2013, The Author(s).