The slash distribution is often used as a challenging distribution for a statistical procedure. In this article, we define a skewed version of the slash distribution in the multivariate setting and derive several of its properties. The multivariate skew-slash distribution is shown to be easy to simulate from and can therefore be used in simulation studies. We provide various examples for illust...

We consider a Laplace operator on a random graph consisting of infinitely many loops joined symmetrically by intervals of unit length. The arc lengths of the loops are considered to be independent, identically distributed random variables. The integrated density of states of this Laplace operator is shown to have discontinuities provided that the distribution of arc lengths of the loops has a n...

We consider a renewal jump-diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin probabilities and related quantities, in models with light...

We consider a processor shared M/M/1 queue that can accommodate at most a finite number K of customers. We give an exact expression for the sojourn time distribution in the finite capacity model, in terms of a Laplace transform. We then give the tail behavior, for the limit K → ∞, by locating the dominant singularity of the Laplace transform. keywords: finite capacity, processor sharing, sojour...

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension p is large. Gaussian graphical models provide an important tool in describing conditional independence through presence or absence of the edges in the underlying graph. A popular non-Bayesian method of estimating a graphical structure is given by the gr...

This work aims at comparing two models of fuzzy distribution: Normal and Laplace, whenever they are inside the context of possibilistic mean-variance model described by Li et al. in [6], where fuzzy Normal distribution is used. We propose to make a comparison using their model, but instead we apply fuzzy Laplace distribution. We also demonstrate the theorems which are necessary for the inclusio...

Brownian-Laplace motion is a Lévy process which has both continuous (Brownian) and discontinuous (Laplace motion) components. The increments of the process follow a generalized normal Laplace (GNL) distribution which exhibits positive kurtosis and can be either symmetrical or exhibit skewness. The degree of kurtosis in the increments increases as the time between observations decreases. This an...

Abstract In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time cdf) can be computed when the Laplace transform values of component pdf...

In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time cdf) can be computed when the Laplace transform values of component pdf’s (e.g.,...

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension p exceeds the sample size n. Gaussian graphical models provide an important tool in describing conditional independence through presence or absence of the edges in the underlying graph. A popular non-Bayesian method of estimating a graphical structure i...