呂育道臺灣大學：資訊工程學研究所林宜禎Lin, I-ChenI-ChenLin2007-11-262018-07-052007-11-262018-07-052007http://ntur.lib.ntu.edu.tw//handle/246246/53643The inverse normal cumulative distribution function does not have a close form. Several algorithms for evaluating (or approximating) the inverse normal cumulative distribution function have been proposed. The aim of the thesis is to compare a few numerical methods of the inverse normal cumulative distribution function, which are used for calculating approximate values of the inverse normal cumulative distribution function. They include the built-in function in EXCEL, a numerical method by Peter J. Acklam, and a numerical method by Moro. The numerical method of Moro is implemented with MATLAB in this thesis. Related errors of the above-mentioned numerical methods are analyzed in the current thesis as well.Contents 口試委員會審定書......................................................................i Abstract………………………………………………………..ii 1 Introduction……………......................................................1 1.1 Introduction…………………………………………….1 1.2 Organization of This Thesis……………………………2 2 Background………………………………………………...3 2.1 Normal Cumulative Distribution Function…………….3 2.2 Inverse Normal Cumulative Distribution Function……4 3 Numerical Methods of the Inverse Normal Cumulative Distribution Function……………………………………...6 3.1 Numerical Method of Acklam…………………………6 3.2 Numerical Method of Moro……………………………7 4 Numerical Results………………………………………….9 4.1 Approximating Values of the Inverse Normal Cumulative Distribution Function with Probabilities Having Lower Precision………………………………………………………...9 4.2 Approximating Values of the Inverse Normal Cumulative Distribution Function with Probabilities Closer to Zero………9 4.3 Testing the Approximating Values in the Numerical Method of Moro.........................................................................................10 5 Conclusions…………………………………………….....12 Bibliography………………………………………………….14 Appendix……………………………………………………...15 Appendix A MATLAB Code of the Numerical Method of Acklam……………………………………………….15 Appendix B MATLAB Code for Implementing the Numerical Method of Moro……………………………………...17 Appendix C Approximating Values of Numerical Methods in the Central Region……………………………………….19 Appendix D Approximating Values of Numerical Methods in the Lower Region………………………………………...32594375 bytesapplication/pdfen-US反向常態累加分布函數數值方法EXCELMATLABAcklamMoroInverse normal cumulative distribution functionnumerical methodthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/53643/1/ntu-96-R91922046-1.pdf