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.

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.

Abstract: Let {(Xi , Yi), i ≥ 1} be a sequence of bivariate random variables from a continuous distribution. If {Rn, n ≥ 1} is the sequence of record values in the sequence of X’s, then the Y which corresponds with the nth record will be called the concomitant of the nth-record, denoted by R[n] . In FGM family, we determine the amount of information contained in R[n] and compare it with amount of information given in Rn. Also, we show that the Kullback-Leibler distance among the concomitants of record values is distribution-free. Finally, we provide some numerical results of mutual information and Pearson correlation coefficient for measuring the amount of dependency between Rn and R[n] in the copula model of FGM family.