Research On High Accuracy Numerical Computation Of Normal Distribution Integral

As a common probability problem in the nature and scientific experiments, thenormal distribution is one of the hot spot research subject between mathematicalstatistics and scientific experiments data analysis. Especially, in the fuzzy theory,random question and uncertainty analysis of the test, based on normal distributionmethods of analysis to the solutions to determine problems, it has an importantmathematics guidance meaning. Univariate normal distribution theory and algorithm aregreat developing and tend to mature, due to the theoretical and practical aspects of theneed, In recent years, people begin to pay close attention to the multidimensionalrandom variable of normal distribution problems. However,owing to multivariatenormal distribution integral function is relatively complex, it must rely on numericalcalculation methods to get the required distribution function value. So the research ofnumerical integration multidimensional normal distribution has certain theoretical andpractical significance.Firstly, this paper simply introduces the normal distribution theory and presentsituation of the study, analyses the existing algorithm and puts forward the question ofthe study. Then, makes a division of integral area, uses the method of integration byparts and the rule of Gauss-Legendre integration, A double precision algorithm for thenormal distribution is presented. Based on the thought of univariate normal distribution,the integral, in the formula of calculating in bivariate and trivariate normal distribution,also uses Gauss-Legendre for product rules, it greatly improve the existing precision.Finally, because the multidimensional integral function of normal distribution isappropriate complicated, An effective method is reducing the dimensions of theparameters. This paper provides four dimension and five dimension normal distribution,and the calculation error is single accuracy. In one word, no matter low dimensional ormultidimensional normal distribution has a strong suitability in calculation accuracyrequirements.