Bayesian Analysis of Record Statistics Based on Generalized Inverted Exponential Model

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.

Reliability Estimation in Multicomponent Stress-Strength for Generalized Inverted Exponential Distribution Based on Ranked Set Sampling

“…Studies about the GIE distribution were discussed by several researchers (for instance see [31][32][33][34][35]). Note that; for 1,  = the CDF (Equation ( 3)) reduces to the IE distribution.…”

Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

“…Combining the likelihood function in (6) and the conditional prior in (20), we get the conditional posterior of (β | α � α j ) as follows:…”

“…Record values appeared naturally in many real-life applications such as data relating to sport, weather, and lifetesting studies. Many authors studied record values and the associated statistics such as [1][2][3][4][5][6]. Furthermore, there are several studies which discussed some inferential methods based on record values for the Rayleigh [7,8], Weibull [9], inverse Weibull [10,11], exponentiated Family [12,13], Lomax [14,15], power Lindley model [16], exponentiated Weibull [17,18], and normal distribution [19].…”

On estimation of stress-strength reliability using lower record values from odd generalized exponential: Exponential distribution

“…for Bayesian comparison of record values based on generalized exponential distribution were considered in [2]. Also, authors found Bayesian analysis for record data Based on Generalized Inverted Exponential Model which considered in [3]. For finding interval estimation for Inverse Rayleigh Distribution based on lower record see [4].…”

“…Figure 2: MSEs OF MLE AND BAYES ESTIMATORS WHEN R=0.75 Shows that the MSEs of MLE and BAYES estimators decrease as n and m are increase at R=0.75, also, MSEs of MLE is smallest than MSEs of BayesFor Real data figures[3,4] …”