Strengthened stability inequalities for mean width and ℓ-norm of convex bodies with fixed John or Löwner ellipsoids, and for convex hulls of centered isotropic measures on the sphere.
Bounding Standard Gaussian Tail Probabilities
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abstract
We review various inequalities for Mills' ratio (1 - \Phi)/\phi, where \phi and \Phi 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.
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math.MG 1years
2020 1verdicts
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Strengthened inequalities for the mean width and the $\ell$-norm
Strengthened stability inequalities for mean width and ℓ-norm of convex bodies with fixed John or Löwner ellipsoids, and for convex hulls of centered isotropic measures on the sphere.