Differentiation of probability functions: The transformation method

DOI10.1016/0898-1221(95)00113-1zbMath0834.60094OpenAlexW2090905570MaRDI QIDQ1904190

Kurt Marti

Publication date: 25 March 1996

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(95)00113-1

zbMATH Keywords

asymptotic expansionintegral transformationLaplace integraldifferentiation of probability functions

Mathematics Subject Classification ID

Reliability, availability, maintenance, inspection in operations research (90B25) Applications of renewal theory (reliability, demand theory, etc.) (60K10)

Related Items (14)

A discussion of probability functions and constraints from a variational perspective ⋮ Differentiation of probability functions: The transformation method ⋮ Derivatives of probability functions: unions of polyhedra and elliptical distributions ⋮ Eventual convexity of probability constraints with elliptical distributions ⋮ A relaxation-based probabilistic approach for PDE-constrained optimization under uncertainty with pointwise state constraints ⋮ Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization ⋮ (Sub-)differentiability of probability functions with elliptical distributions ⋮ A characterization of the subdifferential of singular Gaussian distribution functions ⋮ On the Convexity of Level-sets of Probability Functions ⋮ Gradient formulae for nonlinear probabilistic constraints with non-convex quadratic forms ⋮ Generalized Differentiation of Probability Functions Acting on an Infinite System of Constraints ⋮ Star-shaped approximation approach for stochastic programming problems with probability function ⋮ (Sub-)Gradient Formulae for Probability Functions of Random Inequality Systems under Gaussian Distribution ⋮ Generalized differentiation of probability functions: parameter dependent sets given by intersections of convex sets and complements of convex sets

Cites Work

• Bonferroni inequalities
• Asymptotic approximations for multivariate integrals with an application to multinormal probabilities
• Differentiation of probability functions: The transformation method
• Evaluation of a special multivariate gamma distribution function
• A differentiation formula for integrals overseas given by inclusion
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Differentiation of probability functions: The transformation method