A Four-Moments Alternative to Simulation for a Class of Stochastic Management Models

This paper presents a computational alternative to simulation for a large class of stochastic management models involving functions of random variables. An example of a model in this class is the well-known "risk analysis" problem studied by Hertz and Hillier. Our computational approach includes i a versatile framework to describe the univariate and dependence characteristics of a model's random variables, and ii formulas for computing the central moments of the model's objective variable. The usefulness of these central moments in decision making is then illustrated and discussed.

[1]  Franklin A. Graybill,et al.  Introduction to the Theory of Statistics, 3rd ed. , 1974 .

[2]  Samuel Eilon,et al.  Sampling Procedures for Risk Simulation , 1973 .

[3]  L. R. Shenton,et al.  Approximate percentage points for Pearson distributions , 1979 .

[4]  Lynn E. Bussey,et al.  Net Present Value from Complex Cash Flow Streams by Simulation , 1971 .

[5]  Marcel K. Richter,et al.  Cardinal Utility, Portfolio Selection and Taxation , 1960 .

[6]  Bruce W. Schmeiser,et al.  Methods for modelling and generating probabilistic components in digital computer simulation when the standard distributions are not adequate: A survey , 1977, WSC '77.

[7]  L. R. Shenton,et al.  Further approximate pearson percentage points and Cornish-Fisher , 1979 .

[8]  N. L. Johnson,et al.  Table of percentage points of Pearson curves, for given √β1 and β2, expressed in standard measure , 1963 .

[9]  N. L. Johnson,et al.  Systems of Frequency Curves , 1969 .

[10]  S. J. Pretorius,et al.  SKEW BIVARIATE FREQUENCY SURFACES, EXAMINED IN THE LIGHT OF NUMERICAL ILLUSTRATIONS , 1930 .

[11]  J. G. Bryan,et al.  Applications of probability and random variables , 1974 .

[12]  Yvan Allaire.  A model for the evaluation of risk and additional information in new product decisions , 1975 .

[13]  Irving Kaplansky,et al.  A Common Error concerning Kurtosis , 1945 .

[14]  A STOCHASTIC COST VOLUME PROFIT ANALYSIS , 1973 .

[15]  Karl Pearson,et al.  THE FIFTEEN CONSTANT BIVARIATE FREQUENCY SURFACE , 1925 .

[16]  D. E. Farrar,et al.  The investment decision under uncertainty , 1962 .

[17]  B. Wagle,et al.  A Statistical Analysis of Risk in Capital Investment Projects , 1967 .

[18]  J. K. Ord,et al.  The Discrete Student's $t$ Distribution , 1968 .

[19]  Charles S. Tapiero,et al.  Linear Breakeven Analysis Under Risk , 1975 .

[20]  Frederick S. Hillier,et al.  A Basic Model for Capital Budgeting of Risky Interrelated Projects , 1971 .

[21]  H. O. Hartley,et al.  Biometrika Tables for Statisticians, Vol. 2 , 1973 .

[22]  Egon S. Pearson,et al.  Some problems arising in approximating to probability distributions, using moments , 1963 .

[23]  LeRoy T. Boyer,et al.  PROBABLISTIC APPROACH TO ESTIMATING AND COST CONTROL , 1974 .

[24]  N L JOHNSON,et al.  Bivariate distributions based on simple translation systems. , 1949, Biometrika.

[25]  J. C. Hayya,et al.  On Normal Approximations of the Frequency Functions of Standard Forms Where the Main Variables are Normally Distributed , 1972 .

[26]  E. King,et al.  An Alternative to Monte Carlo Sampling in Stochastic Models , 1975 .