We study control variate estimation where the control mean itself is estimated. Control variate estimation in simulation experiments can significantly increase sampling efficiency, and has traditionally been restricted to cases where the control has a known mean. In a previous paper (Schmeiser, Taaffe, and Wang 2000), we generalized the idea of control variate estimation to the case where the c...

In this paper the interest is to elaborate on generalization of bivariate association measures, namely Spearman’s rho, Kendall’s tau, Blomqvist’s beta and Gini’s gamma, for a general dimension d≥2. Desirable properties axioms such generalizations are discussed, where special attention given impact addition of: (i) an independent random variable vector; (ii) conical combination all components; (...

This paper demonstrates that the logarithm of the variate itself can be used in the calculation of differential entropy among random variables known to be multiples and powers of a common underlying variate. It also presents a function that gives the entropy of these related variates, using only statistics of the logarithm of the variate plus a constant, regardless of the nature or the paramete...

Consider a population of particles and k fixed particle classifications labeled type 1, type 2, ... , type k. Suppose that to each classification there corresponds exactly one k-variate p.g.f. and that each particle of the population is classified by one and only one type. Further, assume that after each unit of time, each particle, independently of the other particles, splits or disintegrates ...

This paper presents a comparative study on the application of different numerical methods for the solution of the dynamic bi-variate population balance equation (PBE) in batch particulate systems. Specifically, particulate processes operating under the combined action of particle aggregation and/or particle growth are examined. In order to solve the bi-variate PBE the Galerkin finite element me...

The Monty Python Method for generating random variables takes a decreasing density, cuts it into three pieces, then, using area-preserving transformations, folds it into a rectangle of area 1. A random point (x; y) from that rectangle is used to provide a variate from the given density, most of the time as x itself or a linear function of x. The decreasing density is usually the right half of a...