Review on Order Statistics and Record Values from F^{α} Distributions

Abstract

Abstract: Both order statistics and records arise naturally in many fields of studies such as climatology, sports, science, engineering, medicine, traffic, and industry, among others. Studies of their properties and applications play important roles in many areas of statistical research, for example, statistical inference, nonparametric statistics, among others. In recent years, the F^{α} distributions have been widely studied in statistics because of their wide applicability in the modeling and analysis of life time data. An absolutely continuous positive random variable X is said to have an F^{α} or exponentiated distribution if its cumulative distribution function (cdf) is given by G(x)=F^{α}(x)=[F(x)]^{α}, α>0, x>0, which is the αth power of the base line distribution function F(x). Many researchers and authors have developed various classes of F^{α} distributions. It appears from the literature that not much attention has been paid to the analysis of record values and order statistics from these members of F^{α} family of distributions, and, therefore, need further and special investigation. In this paper, some distributional properties of order statistics and record values from F^{α} distributions are reviewed. We hope that the findings of this paper will be a useful for the practitioners in various fields of studies and further enhancement of research in order statistics and record value theory, and their applications.