The sharp one-dimensional convex sub-Gaussian comparison constant c_star is given explicitly by a system of one-dimensional equations, numerically ≈2.30952, and attained by an extremal distribution saturating the tail bound.
Stegun, editors.Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, volume 55 ofApplied Mathematics Series
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The sharp one-dimensional convex sub-Gaussian comparison constant
The sharp one-dimensional convex sub-Gaussian comparison constant c_star is given explicitly by a system of one-dimensional equations, numerically ≈2.30952, and attained by an extremal distribution saturating the tail bound.