Three methods of approximating the sum lognormal variates to a distribution were studied. They Wilkinson approximation, Monte Carlo version approximation and using estimated maximum likelihood parameters. The generated empirically simulation based on several conditions such as number in sum, sample points variates, are independent identically distributed (IID) also not (NIID) with Evaluation al...

This article discusses statistical methods for the analysis of multivariate data in experiments with a relatively small number of subjects. Methods based on the assumption of multivariate normality have power that decreases rapidly as the number of variates increases for a fixed sample size. In some investigations, the number of variates exceeds the sample size creating an awkward dilemma in cl...

Multivariate Student importance sampling is a commonly used technique for Bayesian integration problems. For many problems, for example, when the inte-grand has ellipsoidal symmetry, it is a feasible and perhaps preferable, integration strategy. It is widely recognized , however, that the methodology suuers from limitations. We examine the methodology in conjunction with various variance reduct...

This paper presents a novel learning algorithm that nds the linear combination of one set of multi-dimensional variates that is the best predictor, and at the same time nds the linear combination of another set which is the most predictable. This relation is known as the canonical correlation and has the property of being invariant with respect to a ne transformations of the two sets of variate...

Phase-type (PH) distributions are being used to model a wide range of phenomena in performance and dependability evaluation. The resulting models may be employed in analytical as well as in simulationdriven approaches. Simulations require the efficient generation of random variates from PH distributions. PH distributions have different representations and different associated computational cost...

Stochastic models based on matrix exponential structures, like matrix exponential distributions and rational arrival processes, have gained popularity in analytical models recently. However the application of these models in simulation based evaluations is not as widespread yet. One of the possible reasons is the lack of efficient random variates generation methods. In this paper we propose met...

Combined control variates and importance sampling variance reduction and its two-fold optimality are investigated. Two-time-scale stochastic approximation algorithm is applied in parameter search for the combination and almost sure convergence of the algorithm to the unique optimum is proved. The parameter search procedure is further incorporated into adaptive Monte Carlo simulation, and its la...