Type II Half Logistic Family of Distributions with Applications

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.

In this paper, we introduced a generalization of the raised cosine distribution. We also provided its several distributional properties and characterizations, including percentiles and some applications.

Three parameters Birnbaum-Saunders, BS (3P), distribution is an important statistical model which is useable in the fields of both pure and applied sciences. Since its inception, Birnbaum-Saunders (BS) distribution has received a considerable attention in view of its wide applications in many areas of research in applied sciences, such as engineering science, earth science, environmental science, medical science, material fatigue and reliability studies. The objective of this paper is a statistical analysis of the three parameter Birnbaum-Saunders, BS (3P), distribution and to draw some inferences on it. Several new distributional properties of this distribution have been discussed. Based on these distributional properties, we have established several new characterization results of the three-parameter Birnbaum-Saunders distribution. Finally, applications to some real-life data sets are analyzed to show the usefulness of this distribution. The results of this article will be useful for the researchers, scientists, and statisticians in fields of theoretical and applied sciences.