Application of Esscher Transformed Laplace Distribution in Web Server Data
Dais George, Sebastian George · Journal of Digital Information Management · 2011
In this article, we introduce an alternative distri- bution, 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 dis- tributed 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.