Derivatives of probability functions and some applications

Probability functions depending upon parameters are represented as integrals over sets given by inequalities. New derivative formulas for the intergrals over a volume are considered. Derivatives are presented as sums of integrals over a volume and over a surface. Two examples are discussed: probability functions with linear constraints (random right-hand sides), and a dynamical shut-down problem with sensors.

[1]  Y. Ermoliev,et al.  The Minimization of Semicontinuous Functions: Mollifier Subgradients , 1995 .

[2]  W E Vesely,et al.  Study of operational risk-based configuration control , 1991 .

[3]  Ulrich Dieter,et al.  Discrete Optimization Approximating k-cuts using network strength as a Lagrangean relaxation , 2000 .

[4]  Pierre L'Ecuyer.  Gradient estimation via perturbation analysis, by Paul Glasserman, Kluwer, Boston. MA, 1991, 221 pp , 1994, Networks.

[5]  D. P. Gaver,et al.  Detecting component failure potential using proportional hazard model , 1989 .

[6]  S. Uryas'ev,et al.  Differentiability of the integral over a set defined by inclusion , 1988 .

[7]  Paul Glasserman,et al.  Gradient Estimation Via Perturbation Analysis , 1990 .

[8]  Ramavarapu S. Sreenivas,et al.  Augmented infinitesimal perturbation analysis: An alternate explanation , 1992, Discret. Event Dyn. Syst..

[9]  Reuven Y. Rubinstein,et al.  Sensitivity analysis of discrete event systems by the “push out” method , 1992, Ann. Oper. Res..

[10]  Stan Uryasev,et al.  Optimal Operational Strategies for an Inspected Component - Statement of the Problem , 1990 .

[11]  Xi-Ren Cao,et al.  Perturbation analysis of discrete event dynamic systems , 1991 .

[12]  Yu. Emroliev,et al.  Stochastic Quasigradient Methods , 1988 .

[13]  Charles Leake,et al.  Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method , 1994 .

[14]  P. Bjerager,et al.  Methods for Structural Reliability Computations , 1991 .

[15]  Stan Uryasev,et al.  Optimal Operational Strategies for an Inspected Component - Solution Techniques , 1991 .

[16]  S. Uryasev.  Derivatives of probability functions and integrals over sets given by inequalities , 1994 .

[17]  J. Simon,et al.  Second variations for domain optimization problems , 1989 .

[18]  S. Uryasev.  A differentiation formula for integrals overseas given by inclusion , 1989 .

[19]  Niels Olhoff,et al.  Optimization Methods in Structural Design , 1982 .

[20]  Vesely.  Approaches for age-dependent probabilistic safety assessments with emphasis on prioritization and sensitivity studies , 1992 .

[21]  Tamás Szántai,et al.  A new multivariate gamma distribution and its fitting to empirical streamflow data , 1978 .