Bivariate and Bilateral Gamma Distributions

Reliability for Some Bivariate Gamma Distributions

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R = Pr(X < Y). The algebraic form for R = Pr(X < Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when (X ,Y) follows a bivari...

Asymmetric Univariate and Bivariate Laplace and Generalized Laplace Distributions

Alternative specifications of univariate asymmetric Laplace models are described and investigated. A more general mixture model is then introduced. Bivariate extensions of these models are discussed in some detail, with particular emphasis on associated parameter estimation strategies. Multivariate versions of the models are briefly introduced.

Bilateral Gamma Distributions and Processes in Financial Mathematics

We present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma process as well as term structure models driven by bilateral Gamma processes an...

Bivariate Beta Distributions and Beyond

Modeling with Bivariate Geometric Distributions

We study systems with several components which are subject to different types of failures. Examples of such systems include twin engines of an airplane or the paired organs in a human body. We find that such a system, using conditional arguments, can be characterized as multivariate geometric distributions. We prove that the characterizations of the geometric model can be achieved using conditi...