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We review various inequalities for Mills' ratio (1 - \Phi)/\phi, where \phi and \Phi denote the standard Gaussian density and distribution function, respectively.
Values of Mills’ ratio of area to bounding ordinate of the normal probability integral for large values of the argument
R.D. Gordon · 1941
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An inequality for MillsÕ ratio
Z.W. Birnbaum · 1942
Earlier work this paper cites.
Some inequalities on Mills’ ratio and related functions
M.R. Sampford · 1953
Earlier work this paper cites.
Inequalities for the normal integral including a new continued fraction
L.R. Shenton · 1954
Earlier work this paper cites.
Elementary inequalities for Mill’s ratio
Y. Komatu · 1955
Cited alongside, same era.
A remark on “Elementary inequalities for Mill’s ratio” by Y. Komatu
H.O. Pollak · 1956
Cited alongside, same era.
Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (10th printing)
M. Abramowitz · 1972
Cited alongside, same era.
Diffusion Processes and Their Sample Paths
K. Ito · 1974
Cited alongside, same era.
A nonsymmetric correlation inequality for Gaussian measure
S.J. Szarek · 1999
Later among the works it cites.
Inequalities related to the error function
O. Kouba · 2006
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MillsÕ ratio: Monotonicity patterns and functional inequalities
A. Baricz · 2008
Later among the works it cites.
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