In this paper, we consider a perturbed compound Poisson risk model with two-sided jumps. The downward jumps represent the claims following an arbitrary distribution, while the upward jumps are also allowed to represent the random gains. Assuming that the density function of the upward jumps has a rational Laplace transform, the Laplace transforms and defective renewal equations for the discount...

We use the Method of Collective Marks to analyze some time-dependent processes in the M/G/1 queue with single and multiple vacations. With the server state specified at a fixed time t > 0, the Laplace transforms with respect to t of mixed transforms for the joint distribution of the number of departures by time t, the queue length, the virtual waiting time, the elapsed and remaining service/vac...

We propose a Laplace stochastic frontier model as an alternative to the traditional model with normal errors. An interesting feature of the Laplace model is that the distribution of inefficiency conditional on the composed error is constant for positive values of the composed error, but varies for negative values. Therefore, it may be ideally suited for analyzing industries with many forms on o...

In this paper, the lognormal distribution is studied, and a new series representation proposed. This uses powers of bilinear function. From it, simplified form obtained used to compute Laplace transform distribution.

Here x0 ≥ 0 is the initial capital, c > 0 is the premium income per unit of time, N = {Nt, t ≥ 0} is an homogeneous Poisson process with rate λ and {Rk, k = 1, 2, . . .} is a sequence of i.i.d. random variables independent ofN . Henceforth we suppose that R1 has exponential distribution with mean 1/r. Our goal is to calculate explicit expressions for the distributions of the random variables su...

Measurements of chromosomal changes provided using the modern single nucleotide polymorphism (SNP) array technology are accompanied with extensive noise. This makes difficulties in the estimation of genome copy number variations (CNVs) essential for human life. We propose an efficient algorithm for computing the confidence upper and lower boundary limits in order to guarantee an existence of ge...

In this paper, we develop a recursive method to derive an exact numerical and nearly analytical representation of the Laplace transform of the transition density function with respect to the time variable for time-homogeneous diffusion processes. We further apply this recursion algorithm to the pricing of mortality-linked derivatives. Given an arbitrary stochastic future lifetime T, the probabi...

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the...

This paper introduces, investigates, and discusses the γ-order generalized lognormal distribution (γ-GLD). Under certain values of the extra shape parameter γ, the usual lognormal, log-Laplace, and log-uniform distribution, are obtained, as well as the degenerate Dirac distribution.The shape of all themembers of the γ-GLD family is extensively discussed.The cumulative distribution function is e...

Fourier and hyperbolic models of heat transfer on a fin that is subjected to a periodic boundary condition are solved analytically. The differential equation in Fourier and non-Fourier models is solved by the Laplace transform method. The temperature distribution on the fin is obtained using the residual theorem in a complex plan for the inverse Laplace transform method. The thermal shock is ge...