scientific article; zbMATH DE number 1740985

zbMath1010.62015MaRDI QIDQ4331174

Iosif Pinelis

Publication date: 10 June 2002

Full work available at URL: https://eudml.org/doc/122588

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zbMATH Keywords

monotonicitycomplementary error functionfailure raterelative errorPade approximationMills' ratiol'Hospital's rulecontinuous fractions

Mathematics Subject Classification ID

Padé approximation (41A21) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Inequalities for sums, series and integrals (26D15) Approximations to statistical distributions (nonasymptotic) (62E17) Monotonic functions, generalizations (26A48) Continued fraction calculations (number-theoretic aspects) (11Y65) Convergence and divergence of continued fractions (40A15) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

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Memory Capacity of Neural Networks with Threshold and Rectified Linear Unit Activations ⋮ Tail dependence of the Gaussian copula revisited ⋮ New sharp approximations involving incomplete gamma functions ⋮ Approximating Mills ratio ⋮ On approximations of value at risk and expected shortfall involving kurtosis ⋮ On the norming constants for normal maxima ⋮ Properties of the probability density function of the non-central chi-squared distribution ⋮ Mills' ratio: Monotonicity patterns and functional inequalities ⋮ Monotonicity rule for the quotient of two functions and its application ⋮ Some new upper and lower bounds for the Mills ratio ⋮ On the hazard function of Birnbaum-Saunders distribution and associated inference ⋮ A generalization of L'Hospital-type rules for monotonicity and its application ⋮ General Smile Asymptotics with Bounded Maturity ⋮ On approximating Mills ratio

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