International Journal on Advanced Science, Engineering and Information Technology, Vol. 8 (2018) No. 2, DOI:10.18517/ijaseit.8.2.3506

Bayesian Analysis of Record Statistics Based on Generalized Inverted Exponential Model

Amal S. Hassan, Marwa Abd-Allah, Heba F. Nagy

Abstract

In some situations, only observations that are more extreme than the current extreme value are recorded. This kind of data is called record values which have many applications in a lot of fields. In this paper, the Bayesian estimators using squared error and LINEX loss functions for the generalized inverted exponential distribution parameters are considered depending on upper record values and upper record ranked set sampling. The Bayes estimates and credible intervals are derived by considering the independent gamma priors for the parameters. The Markov Chain Monte Carlo (MCMC) method is developed due to the lack of explicit forms for the Bayes estimates.  A simulation study is implemented to compute and compare the performance of estimators in both sampling schemes with respect to relative absolute biases, estimated risks and the width of credible intervals.

Keywords:

upper record ranked set sample; Bayesian estimator; squared error (SE) loss function; linear exponential (LINEX) loss function; Markov Chain Monte Carlo

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