Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Objects. The ~ b s t rac t ~ b j ect forms the fundamental base class for the entire design and all other classes are derived from this base class. The Abstract Object class defines and characterizes all the essential properties every class in this 404 OBJECT-ORIENTED SIMULATION

Handbook of Simulation

(1992). Time Series—A Biostatistical Introduction. Technometrics: Vol. 34, No. 2, pp. 229-230.

Time Series—A Biostatistical Introduction

Methods of Feasible Directions. By G. Zoutendijk. Pp. 126. 30s. 1960. (D. van Nostrand Co. London)

Coordination mechanisms of supply chain systems

Practical solutions to complicated sampling problems can often be found through the use of polynomial approximators. The approximators can yield exact expressions for (approximate) statistical properties, such as moments, obviating the need for sampling; on the other hand, should sampling be used, the approximators can be applied as control variates to sharpen Monte Carlo results. In this paper we give exact expressions for the first three moments of second order polynomials of independent and identically distributed random variables. The utility of these polynomials is illustrated in three examples: The first concerns the evaluation of the moments of the sample variance, the second investigates properties of a present value when interest rates vary, and the third involves control variates in a complicated sampling problem with nonlinear regression.

Moments of second order polynomials with simulation applications

The computer in measuring judicial productivity

Control variates can be applied to Monte Carlo sampling experiments to improve the precision of the results. This method is especially useful in statistical problems were low order approximators of a particular variate of interest are available and possibly several statistical properties of the variate are to be investigated. In this paper a control variate scheme based on the linear approximator s of the nonlinear parameter estimator (

Control variates in nonlinear regression

We describe single-stage and closed sequential procedures for selecting the most probable cell of a multinomial distribution. These procedures are then reformulated as nonparametric techniques for selecting the best one of a number of competing simulated systems or alternatives. We discuss performance characteristics of the procedures and make recommendations concerning their use.

/pdf/multinomial-selection-procedures-for-use-in-simulations-540g16wo7e.pdf

Multinomial selection procedures for use in simulations

Linear control variates provide a convenient means for variance reduction in a wide variety of simulation and Monte Carlo sampling problems. The effectiveness of control variates can often be improved using appropriate transformations which increase the correlation between the primary variate and the transformed control variate. Possible transformations include polynomials, the Box-Cox family of power transformations, and the inverse-normal probability transformation. Here we consider generalized transformations using cubic splines which provide a virtually unrestricted source of transformations. To illustrate the transformation methodology, a nonlinear regression problem is used. In the illustration, the transformed control is compared to the control when estimating the mean of the sampling distribution of the estimated parameters.

/pdf/augmenting-linear-control-variates-using-transformations-a1itm0chgu.pdf

James J. Swain

Papers

Moments of second order polynomials with simulation applications

The computer in measuring judicial productivity

Control variates in nonlinear regression

Multinomial selection procedures for use in simulations

Augmenting Linear Control Variates Using Transformations