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Original Articles

New Chebyshev Polynomial Approximations to Mills' Ratio

Pages 647-654 | Published online: 10 Apr 2012

References

  • Clenshaw , C. W. 1955 . “A note on the summation of Chebyshev series,” . MTAC , 9 : 118 – 20 .
  • Clenshaw , C. W. 1962 . “Chebyshev series for mathematical functions,” . In Mathematical Tables , Vol. 5 , London : HMSO .
  • Gray , H. L. and Schucany , W. R. 1968 . “On the evaluation of distribution functions,” . Journal of the American Statistical Association , 63 : 715 – 20 .
  • Kiel , D. J. , Johnson , D. E. and Smith , R. E. “Partitioned polynomials—an approach towards equilibrium between accuracy and speed in primary mathematical functions,” . ACM National Conference . Digest Tech. Papers
  • Ray , W. D. and Pitman , A. E. N. T. 1963 . “Chebyshev polynomials and other new approximations to Mills' ratio,” . Annals of Mathematical Statistics , 34 : 842 – 902 .
  • Ruben , H. 1936 . “A convergent asymptotic expansion for Mills' ratio and the normal probability integral in terms of rational functions,” . Mathematische Annalen , 151 : 355 – 64 .
  • Ruben , H. 1964 . “Irrational fraction approximations to Mills' ratio,” . Biometrika , 51 : 339 – 45 .

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