A uniform approximation to the right normal tail integral

被引:28
作者
Bryc, W [1 ]
机构
[1] Univ Cincinnati, Dept Math, Cincinnati, OH 45221 USA
关键词
calculator approximation; cumulative normal distribution; Mill's ratio;
D O I
10.1016/S0096-3003(01)00015-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper presents two simple formulas for approximation of the standard normal right tail probabilities, and indicates the method of computing approximations of higher order. One of the approximations relies on two simple numerical constants, has absolute error of 0.00071 and relative error 0.023; the other uses four numerical constants, has absolute error of 0.000019, the relative error is 0.005 and gives at least two significant digits for probabilities over the entire range 0 less than or equal to z less than or equal to infinity. (C) 2002 Elsevier Science Inc. All rights reserved.
引用
收藏
页码:365 / 374
页数:10
相关论文
共 24 条
[1]  
[Anonymous], 1970, DISTRIBUTIONS STAT C
[2]   CALCULATION OF UNIVARIATE AND BIVARIATE NORMAL PROBABILITY FUNCTIONS [J].
DIVGI, DR .
ANNALS OF STATISTICS, 1979, 7 (04) :903-910
[3]  
FELLER W, 1966, INTRO PROBABILITY, V2
[4]  
Hamaker H.C., 1978, J R STAT SOC C-APPL, V27, P76
[5]  
HART RG, 1966, MATH COMPUT, V20, P600
[6]  
HART RG, 1957, MATH TABLES OTHER AI, V11
[7]  
Hastings C., 1955, APPROXIMATIONS DIGIT
[8]  
Johnson N. L., 1970, DISTRIBUTIONS STAT C, V2
[9]  
KERRIDGE DF, 1976, BIOMETRIKA, V63, P401
[10]  
Laplace P.-S., 1820, THEORIE ANAL PROBABI