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Chebyshev subinterval polynomial approximations for continuous distribution functions
Author(s) -
Tsai HsienTang,
Moskowitz Herbert
Publication year - 1989
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198908)36:4<389::aid-nav3220360405>3.0.co;2-s
Subject(s) - approximation error , chebyshev nodes , minimax approximation algorithm , chebyshev polynomials , spouge's approximation , mathematics , polynomial , approximation theory , equioscillation theorem , chebyshev filter , function (biology) , distribution (mathematics) , simple (philosophy) , function approximation , approximation algorithm , linear approximation , mathematical optimization , mathematical analysis , computer science , orthogonal polynomials , gegenbauer polynomials , artificial neural network , classical orthogonal polynomials , nonlinear system , philosophy , biology , epistemology , quantum mechanics , evolutionary biology , machine learning , physics
An algorithm for constructing a three‐subinterval approximation for any continous distribution function is presented in which the Chebyshev criterion is used, or equivalently, the maximum absolute error (MAE) is minimized. The resulting approximation of this algorithm for the standard normal distribution function provides a guideline for constructing the simple approximation formulas proposed by Shah [13]. Furthermore, the above algorithm is extended to more accurate computer applications, by constructing a four‐polynomial approximation for a distribution function. The resulting approximation for the standard normal distribution function is at least as accurate as, faster, and more efficient than the six‐polynomial approximation proposed by Milton and Hotchkiss [11] and modified by Milton [10].