Review on order statistics and record values from Fα distributions

Abstract

Both order statistics andrecords arise naturally in many fields of studies such as climatology, sports, science, engineering, medicine, traffic, and industry, among others. Study of their properties and applications plays important roles in many areas of statistical research, for example, statistical inference, nonparametric statistics, among others. In recent years, the Fα 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 Fα distribution if its cumulative distribution function is given by G(x) = Fα (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 Fα 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 Fα family of distributions, and, therefore, need further and special investigations. In this paper, some distributional properties of order statistics and record values from Fα distributions are reviewed. We hope that the findings of this paper will be useful for the practitioners in various fields of studies and further enhancement of research in Fα distributions, order statistics, record value theory and their applications.