Journal of Data Science

Abstract: Ranked set sampling and some of its variants have been applied successfully in different areas of applications such as industrial statistics, economics, environmental and ecological studies, biostatistics, and statistical genetics. Ranked set sampling is a sampling method that more efficient than simple random sampling. Also, it is well known that Fisher information of a ranked set sample (RSS) is larger than Fisher information of a simple random sample (SRS) of the same size about the unknown parameter of the underlying distribution in parametric inference. In this paper, we consider the Farlie-Gumbel-Morgenstern (FGM) family and study the information measures such as Shannon’s entropy, Rényi entropy, mutual information, and Kullback-Leibler (KL) information of RSS data. Also, we investigate their properties and compare them with a SRS data.

In this paper we use the maximum likelihood (ML) and the modified maximum likelihood (MML) methods to estimate the unknown parameters of the inverse Weibull (IW) distribution as well as the corresponding approximate confidence intervals. The estimates of the unknown parameters are obtained based on two sampling schemes, namely, simple random sampling (SRS) and ranked set sampling (RSS). Comparison between the different proposed estimators is made through simulation via their mean square errors (MSE), Pitman nearness probability (PN) and confidence length.

Abstract: In this paper, we obtain several estimators of a scale parameter of Morgenstern type bivariate uniform distribution (MTBUD) based on the observations made on the units of the ranked set sampling regarding the study variable Y which is correlated with the auxiliary variable X, when (X, Y ) follows a MTBUD. Efficiency comparisons among these estimators are also made in this work. Finally, we illustrate the methods developed by using a real data set.