Bayesian inference and prediction of the Pareto distribution based on ordered ranked set sampling

Abstract

In this paper, order statistics from independent and non-identically distributed (INID) random variables is used to obtain ordered ranked set sampling (ORSS). Bayesian inference of unknown parameters under a squared error loss function of the Pareto distribution are determined. We compute the minimum posterior expected loss (the posterior risk) of the derived estimates and compare them with those based on the corresponding simple random sample to assess the efficiency of the obtained estimates. Two-sample Bayesian prediction for future observations are introduced by using SRS and ORSS for one-and m-cycle. A simulation study and real data are applied to show the proposed results.

Statistical Prediction Based on Ordered Ranked Set Sampling Using Type-II Censored Data from the Rayleigh Distribution under Progressive-Stress Accelerated Life Tests

“…Te distribution-free prediction intervals for record values and future order statistics were constructed in [27]. In [28,29], it was investigated how to predict unobserved data under a type-II censoring scheme (CS) and how to estimate the parameters of Rayleigh and Pareto distributions using Bayesian methods. Based on type-I CS, the step-stress ALT data were used in [30,31] to estimate the parameters of Rayleigh and exponential distributions.…”

Exact prediction intervals for future exponential and Pareto lifetimes based on ordered ranked set sampling of non-random and random size

“…Moreover, Balakrishnan and Li (2008) proved that the best linear unbiased estimators based on the ORSS are more efficient than the best linear unbiased estimators based on the RSS for the two-parameter exponential, normal, and logistic distributions. Some Bayesian prediction problems based on the RSS and ORSS were studied by Mohie El-Din et al (2015. They got the two-sample Bayesian prediction intervals for the observables from the Pareto distribution based on complete and censored data.…”

“…The prediction intervals for future order statistics based on type II censoring have been studied by many authors, among them are Lawless (1977), Mohie El-Din et al (2015, Patel (1989), Raqab andRaqab andNagaraja (1995).…”

On Concomitants of Ordered Ranked Set Sampling from Morgenstern Family

“…Takahasi and Wakimoto (1968) have presented a more detailed mathematical development for the RSS. During the last three decades, there has been much work on RSS to improve and study the estimation of population parameters, see for example Sinha et al (1996), Samawi et al (1996), Adatia (2000), Al-Saleh and Al-Omari (2002), Shaibu and Muttlak (2004), Balakrishnan and Li (2008), Kadilar et al (2009), Al-Saleh and Samawi (2010), Ozturk (2011), Mohie El-Din et al (2015) and Sadek et al (2015). The prediction problems based on RSS are studied by several authors, for instance Salehi et al (2015), Kotb (2016), Mohie El-Din et al (2017) and Kotb and Raqab (2017).…”