Estimating and validating the cumulative distribution of a function of random variables: Toward the development of distribution arithmetic

Reliable Computing

Volumn 9, Issue 2, 2003, Pages 127-141

  Lodwick, Weldon A ^a   Jamison, K David ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b Watson Wyatt and Company   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; DIGITAL ARITHMETIC; FUNCTIONS; ITERATIVE METHODS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

RANDOM VARIABLES;

LINEAR PROGRAMMING;

EID: 0037382015     PISSN: 13853139     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023090317875     Document Type: Conference Paper

References (20)

1. Berberian, S. K.: Measure and Integration, Chelsea Publishing Company, Bronx, New York, 1970.
2. Berleant, D.: Automatically Verified Reasoning with Both Intervals and Probability Density Functions, Interval Computations 1 (1993), pp. 48-70.
3. Berleant, D. and Goodman-Strauss, C.: Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals, Reliable Computing 4 (2) (1998), pp. 147-165.
4. Breiman, L.: Probability, SIAM, Philadelphia, 1992.
5. Dempster, M. A. H.: An Application of Quantile Arithmetic to the Distribution Problem in Stochastic Linear Programming, Bulletin of the Institute of Mathematics and Us Applications 10 (1974), pp. 186-194.
6. Dempster, M. A. H.: Distributions in Interval and Linear Programming, in: Hansen, E. R. (ed.), Topics in Interval Analysis, Oxford Press, 1969, pp. 107-127.
7. Ferson, S.: Probability Bounds Analysis Software, in: Computing in Environmental Resource Management: Proceedings of a Speciality Conference, Research Triangle Park, NC, December 2-4, 1996, Air and Waste Management Association, Pittsburgh, pp. 669-677.
8. Ferson, S.: Quality Assurance for Monte Carlo Risk Assessment, in: IEEE Proceedings of ISUMA-NAFIPS'95, 1995, pp. 14-19.
9. Ferson, S., Ginzburg, L., and Aķakaya, R.: Whereof One Cannot Speak: When Input Distributions Are Unknown, Risk Analysis, to appear.
10. Jamison, K. D., and Lodwick, W. A.: The Construction of Consistent Possibility and Necessity Measures, Fuzzy Sets and Systems 132 (1) (2002), pp. 1-10.
11. Jamison, K. D., Lodwick, W. A., and Kawai, M.: A Simple Closed Form Estimation for the Cumulative Distribution Function of a Monotone Function of Random Variables, UCD/CCM Report No. 187, 2002.
12. Kaplan, S.: On the Method of Discrete Probability Distributions in Risk and Reliability Calculations - Applications to Seismic Risk Assessment, Journal of Risk 1 (3) (1981), pp. 189-196.
13. Moore, A. S.: Interval Risk Analysis of Real Estate Investment: A Non-Monte Carlo Approach, Freiburger Intervall-Berichte 85 (3) (1985), pp. 23-49.
14. Moore, R. E.: Risk Analysis without Monte Carlo Methods, Freiburger Intervall-Berichte 84 (1) (1984), pp, 1-48.
15. Nickel, K.: Triplex-Algol and Its Applications, in: Hansen, E. R. (ed.), Topics in Interval Analysis, Oxford Press, 1969, pp. 10-24.
16. Ross, S.:A First Course in Probability, Macmillan Publishing Co., New York, 1976.
17. Royden, H. L.: Real Analysis, Prentice Hall, Englewood Cliffs, 1988.
18. Shapiro, M. and Wilcox, D.: Generating Non-Standard Multivariate Distributions with an Application to Mismeasurement in the CPI, Technical Working Paper 196, National Bureau of Economic Research, 1050 Massachusetts Avenue, Cambridge, MA 02138, May 1996.
19. Williamson, R. C.: Interval Arithmetic and Probability Arithmetic, in: Ullrich, C. (ed.), Contributions to Computer Arithmetic and Self-Validating Numerical Methods, J. C. Baltzer AG, IMACS, 1990, pp. 67-80.
20. Williamson, R. C. and Downs, T.: Probabilistic Arithmetic I: Numerical Methods for Calculating Convolutions and Dependency Bounds, International Journal of Approximate Reasoning 4 (1990), pp. 89-158.