Abstract Let f be the density function associated to a matrix-exponential distribution of parameters $(\boldsymbol{\alpha}, T,\boldsymbol{{s}})$ . By exponentially tilting , we find probabilistic interpretation which generalizes one phase-type distributions. More specifically, show that for any sufficiently large $\lambda\ge 0$ $x\mapsto \left(\int_0^\infty e^{-\lambda s}f(s)\textrm{d} s\right)...

Two quadrature-based algorithms for computing the matrix fractional power $A^\alpha$ are presented in this paper. These based on double exponential (DE) formula, which is well-known its effectiveness improper integrals as well treating nearly arbitrary endpoint singularities. The DE formula transforms a given integral into another that suited trapezoidal rule; process, interval transformed an i...

Classic performance evaluation using queueing theory is usually done assuming a stable model in equilibrium. However, there are situations where we interested the transient phase. In this case, main metrics built around model’s state distribution at an arbitrary point time. dependability, significant part of analysis previous work, developed approach to derive distributions some continuous time...

The multidimensional exponential Levy equations are used to describe many stochastic phenomena such as market fluctuations. Unfortunately in practice an exact solution does not exist for these equations. This motivates us to propose a numerical solution for n-dimensional exponential Levy equations by block pulse functions. We compute the jump integral of each block pulse function and present a ...

We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of real and finite square $A$ (and complex ones also). The elementary method developed avoids Jordan canonical form, eigenvectors, resolution any linear system, inversion, polynomial interpolation, integration, functional analysis, generalized Fibonacci sequences. basic tools are Cayley-Hamilton theore...

In this paper, a unified M-estimation method in Yang (2018 Yang, Z. (2018). Unified of fixed-effects spatial dynamic models with short panels. Journal Econometrics 205(2):423–447. doi:https://doi.org/10.1016/j.jeconom.2017.08.019[Crossref], [Web Science ®] , [Google Scholar]) is extended to the matrix exponential panel specification (MESDPS) fixed effects Similar STLE model which includes lag e...