Application of Esscher Transformed Laplace Distribution in Web Server Data

AbstrAct: In this article, we introduce an alternative distribution , namely Esscher transformed Laplace distribution good enough to model the file size distribution of Web servers. It exhibits asymmetry, peakedness and tail heaviness, which are common features of file size data. Esscher transformed Laplace distribution belongs to one parameter regular exponential family. We derive their representations and obtain explicit forms for their densities, distribution functions and quantile functions. Also the probability R = P(X > Y) and an asymptotic confidence interval for R, when X and Y are two independent but not identically distributed Esscher transformed Laplace variables are estimated and its application in the service performance of a Web server is discussed. Extensive simulation studies are carried out to study the performance of these estimators. Finally using real data, we established the goodness of fit of the proposed distribution to the file size distribution of a Web server data.