909 research outputs found
Bayesian Inference For Exponential Distribution Based On Upper Record Range
This paper deals with Bayesian estimations of scale parameter of the
exponential distribution based on upper record range (Rn). This has been done
in two steps; point and interval. In the first step the quadratic, squared
error and absolute error, loss functions have been considered to obtain
Bayesian-point estimations. Also in the next step the shortest Bayes interval
(Hight Posterior Density interval) and Bayes interval with equal tails based on
upper record range have been found. Therefore, the Homotopy Perturbation
Method(HPM) has been applied to obtain the limits of Hight Posterior Density
intervals. Moreover, efforts have been made to meet the admissibility
conditions for linear estimators based on upper record range of the form mRn+d
by obtained Bayesian point estimations. So regarding the consideration of loss
functions, the prior distribution between the conjunction family has been
chosen to be able to produce the linear estimations from upper record range
statistics. Finally, some numerical examples and simulations have been
presented
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