Estimation of \(R=P[Y < X]\) for Burr type XII distribution based on ranked set sampling
Ranked set sampling (RSS) is a statistical technique for data collection that generally leads to more efficient estimators than competitors based on simple random sample (SRS). In the current paper, the estimation of R=P[Y<X] when Y and X are two independent Burr type XII distribution with common known shape parameter c will be considered. Maximum likelihood estimator is proposed to estimate R based on ranked set sampling data. These estimators will be compared in terms of their biases, mean square errors and efficiencies with known estimators based on SRS data. It is shown that the estimators based on RSS are more efficient than the corresponding SRS. The results are illustrated using simulated data.
Keywords: Burr Type XII, Stress Strength Model, Ranked Set Sampling, Method of Maximum Likelihood.
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