Regression Estimators Related to Multinormal Distributions: Computer Experiences in Root Finding Istvan Decik[l] [1] Operations Research Group, Dept. of Differential Equations Technical University of Budapest H-l1l1 Budapest, XI. Muegyetem rkp. 3. email: deak@inf.bme.hu Several simple regression estimators can be constructed to approximate the dis- tribution function of the m-dimensional normal distribution along a line. These functions can be used to find the border points of the feasible region of probability constrained stochastic programming models. Computer experiences show a fast and robust behaviour of the root finding techniques. Keywords: multinormal distribution, stochastic programming, regression estimators, quantile computation 1 Introduction Consider the m-dimensional normal distribution with expected value 0 and correlation matrix R. Its distribution function and density function are given as 4'(h) (1) ¢(z) Computation of the function values 4'(h) is required in numerical optimiza- tion procedures of stochastic programming problems, when the random variables of the model have a joint normal distribution. This is the case in solution pro- cedures of the STABIL stochastic programming model [11] and the two-stage model [9]. Other problems, where computation of (1) is required can be found in diverse areas of statistics and engineering ([1], [6], [4]). K. Marti et al. (eds.), Stochastic Programming Methods and Technical Applications © Springer-Verlag Berlin Heidelberg 1998