Bounding Standard Gaussian Tail Probabilities

@article{Dmbgen2010BoundingSG,
  title={Bounding Standard Gaussian Tail Probabilities},
  author={L. D{\"u}mbgen},
  journal={arXiv: Statistics Theory},
  year={2010}
}
  • L. Dümbgen
  • Published 2010
  • Mathematics
  • arXiv: Statistics Theory
  • We review various inequalities for Mills' ratio (1 - Φ)= O, where O and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds. 

    Figures and Tables from this paper.

    Approximating Mills ratio
    25
    On Dümbgen's exponentially modified Laplace continued fraction for Mill's ratio
    2
    Combinatorial Properties of Mills Ratio
    1
    The Australian Journal of Mathematical Analysis and Applications
    • 2013
    Integer Sequences Connected to the Laplace Continued Fraction and Ramanujan's Identity

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 13 REFERENCES
    Inequalities related to the error function
    9
    A Nonsymmetric Correlation Inequality for Gaussian Measure
    47
    INEQUALITIES FOR THE NORMAL INTEGRAL INCLUDING A NEW CONTINUED FRACTION
    30
    An Inequality for Mill's Ratio
    57
    DIFFUSION PROCESSES AND THEIR SAMPLE PATHS
    746
    Elementary inequalities for Mill’s ratio
    • 1955
    Values of Mills' Ratio of Area to Bounding Ordinate and of the Normal Probability Integral for Large Values of the Argument
    182