Abstract
The aim of this paper is to estimate the parameters of exponentiated Burr type XII distribution (EBXII) based on ranked set sampling (RSS) technique, and also simple random sampling(SRS) is provided by the method of maximum likelihood. Fisher information matrix for both (SRS) and (RSS) for the unknown parameters are derived. Simulation study compared between the estimators of both methods in terms of their biases, mean square errors, and efficiencies. It is shown that the estimators based on RSS are more efficient than those of SRS.
Highlights
The Exponentiated Burr XII (EBXII) is an extended distribution to Burr type XII distribution . this model is an important model for several areas such as actuarial sciences, economic,survival analysis
Al-Hussaini and Hussain(2011) paid a great concern to Exponentiated models in general and Exponentiated Burr type XII in particular. They estimated the parameters of EBXII distribution using type II Censoring, Bayes estimators are provided under complete samples and censored type II samples. ranked set sampling (RSS) is a statistical technique for data collection that generally leads to more efficient estimators than those based on simple random sampling (SRS)
AL-Saleh and AL-Kadiri (2000) considered double ranked set sample (DRSS) as a two-stage sampling technique that increase the efficiency of RSS estimator without increasing set size it is shown that double ranked set sampling is more efficient than RSS
Summary
The Exponentiated Burr XII (EBXII) is an extended distribution to Burr type XII distribution . this model is an important model for several areas such as actuarial sciences , economic ,survival analysis. Al-Hussaini and Hussain(2011) paid a great concern to Exponentiated models in general and Exponentiated Burr type XII in particular They estimated the parameters of EBXII distribution using type II Censoring, Bayes estimators are provided under complete samples and censored type II samples. Abu-Dayyeh and Assrhani (2011) estimate the shape and location parameters of the Pareto distribution based on RSS and SRS and compare between the two methods .the estimation of unknown parameters of normal ,the exponential and gamma distributions using median and extreme ranked set sample was studied by Shaibu and Muttlak (2004). Gurler and Esemen (2017)estimated the parameters of generalized Rayleigh distribution based on simple random sampling and ranked set sampling
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