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.

It is well known that the Laplace-Stieltjes transform of a nonnegative random variable (or vector) uniquely determines its distribution function. We extend this uniqueness theorem by using Muntz-Szasz Theorem and identity for Laplace-Carson transforms The latter appears first time to best our knowledge. In particular, if X Y are two variables with joint H, then H can be characterized suitable s...

2 Neural information processing is noisy 6 2.1 Poisson Processes . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Interval distribution . . . . . . . . . . . . . . . . . . . . . 10 2.1.2 Integration reduces CV . . . . . . . . . . . . . . . . . . . 12 2.1.3 Refractoriness . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 ISI distributions . . . . . . . . . . . . . . . . . . . . . ....

We express the idea of classical competition in a statistical equilibrium model, where the tendency for competition to equalize profit rates results in an exponential power (or Subbotin) distribution. The model supports and extends recent evidence on the Laplace distribution of growth rates in firm size. We also find tent-shaped distributions in the size growth rates of Forbes Global 2000 compa...

We shall first review some non-normal stationary first-order autoregressive models. The models are constructed with a given marginal distribution (logistic, hyperbolic secant, exponential, Laplace, or gamma) and the requirement that the bivariate joint distribution of the generated process must be sufficiently simple so that the parameter estimation and forecasting problems of the models can be...

We address a quantile dependent prior for Bayesian quantile regression. We extend the idea of the power prior distribution in Bayesian quantile regression by employing the likelihood function that is based on a location-scale mixture representation of the asymmetric Laplace distribution. The propriety of the power prior is one of the critical issues in Bayesian analysis. Thus, we discuss the pr...

This article presents a perishable (s; S) inventory system under continuous review at a service facility in which a waiting hall for customers is of nite size M. The arrival instants of customers to the service station constitutes a Poisson process. The life time of each items is assumed to be exponential. All arriving customers demand the rst "essential" service, whereas only some of them dema...