论文信息 - APPROXIMATION TO THE CUMULATIVE NORMAL DISTRIBUTION USING HYPERBOLIC TANGENT BASED FUNCTIONS

APPROXIMATION TO THE CUMULATIVE NORMAL DISTRIBUTION USING HYPERBOLIC TANGENT BASED FUNCTIONS

This paper presents a method for approximation of the stan- dard normal distribution by using hyperbolic tangent based functions. The presented approximate formula for the cumulative distribution de- pends on one numerical coecient only, and its accuracy is admissible. Furthermore, in some particular cases, closed forms of inverse formulas are derived. Numerical results of the present method are compared with those of an existing method.

Beong In Yun | B. Yun

[1] E. Page,et al. Approximations to the Cumulative Normal Function and its Inverse for Use on a Pocket Calculator , 1977 .

[2] George Szekeres,et al. Numerical evaluation of high-dimensional integrals , 1964 .

[3] D. F. Kerridge,et al. Yet another series for the normal integral , 1976 .

[4] Wlodzimierz Bryc,et al. A uniform approximation to the right normal tail integral , 2002, Appl. Math. Comput..

[5] Jinn-Tyan Lin,et al. A Simpler Logistic Approximation to the Normal Tail Probability and its Inverse , 1990 .

[6] P. A. P. Moran,et al. Calculation of the normal distribution function , 1980 .

[7] R. G. Hart. A close approximation related to the error function , 1966 .

[8] H. C. Hamaker,et al. Approximating the Cumulative Normal Distribution and its Inverse , 1978 .

[9] R. M. Norton,et al. Pocket-Calculator Approximation for Areas under the Standard Normal Curve , 1989 .

[10] Gary R. Waissi,et al. A sigmoid approximation of the standard normal integral , 1996 .

[11] David Elliott,et al. Sigmoidal Transformations and the Trapezoidal Rule , 1998 .

[12] Richard J. Bagby,et al. CALCULATING NORMAL PROBABILITIES , 1995 .

[13] John D. Vedder,et al. An invertible approximation to the normal distribution function , 1993 .

[14] A. M. Denisov. On an integral equation of first kind , 1998 .