Geometric Exponential Distributions

The theory and applications of geometric stable laws has been an active area of research in recent years. They are obtained as limiting laws of approximately normalized random sums of i.i.d. random variables. Geometric stable laws are found to be particularly useful in modeling financial assets return data. Mittag-Leffler distribution and Linnik distribution are members of this class. Their applications range from queuing and reliability theories to modeling financial portfolios. They are heavy tailed and have applications in financial modeling also.The main purpose of this book is to provide a rigorous introduction to geometric exponential laws as well as their generalizations and applications with special emphasis on autoregressive time series modeling. The book introduces the concepts of geometric infinite divisibility and various geometric stable distributions like geometric Mittag-Leffler, geometric alpha-Laplace and related distributions.It should be of use for researchers and practitioners in mathematics, statistics, engineering, financial modeling, mathematical finance, stochastic processes, probability theory and applications.