메뉴 건너뛰기




Volumn 41, Issue 3, 2006, Pages 331-342

Computing best-possible bounds for the distribution of a sum of several variables is NP-hard

Author keywords

Best possible bounds; NP hard; Sum of random variables

Indexed keywords

COMPUTATIONAL METHODS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; UNCERTAIN SYSTEMS;

EID: 33644862903     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2005.06.009     Document Type: Article
Times cited : (15)

References (22)
  • 4
    • 0142140760 scopus 로고    scopus 로고
    • Distribution-free risk analysis: I. Range, mean, and variance
    • Applied Biomathematics
    • S. Ferson, D. Myers, D. Berleant, Distribution-free risk analysis: I. Range, mean, and variance, Applied Biomathematics, Technical Report, 2001.
    • (2001) Technical Report
    • Ferson, S.1    Myers, D.2    Berleant, D.3
  • 6
    • 33644850049 scopus 로고    scopus 로고
    • Novel approaches to numerical software with result verification
    • R. Alt, A. Frommer, R.B. Kearfott, W. Luther (Eds.), Numerical Software with Result Verification, International Dagstuhl Seminar, Dagstuhl Castle, Germany, 19-24 January 2003, Revised Papers
    • L. Granvilliers, V. Kreinovich, N. Müller, Novel Approaches to Numerical Software with Result Verification, in: R. Alt, A. Frommer, R.B. Kearfott, W. Luther (Eds.), Numerical Software with Result Verification, International Dagstuhl Seminar, Dagstuhl Castle, Germany, 19-24 January 2003, Revised Papers, Springer Lectures Notes in Computer Science, 2004, vol. 2991, pp. 274-305.
    • (2004) Springer Lectures Notes in Computer Science , vol.2991 , pp. 274-305
    • Granvilliers, L.1    Kreinovich, V.2    Müller, N.3
  • 9
    • 6944233967 scopus 로고    scopus 로고
    • Probabilities, intervals, what next? optimization problems related to extension of interval computations to situations with partial information about probabilities
    • V. Kreinovich Probabilities, intervals, what next? optimization problems related to extension of interval computations to situations with partial information about probabilities Journal of Global Optimization 29 3 2004 265 280
    • (2004) Journal of Global Optimization , vol.29 , Issue.3 , pp. 265-280
    • Kreinovich, V.1
  • 11
    • 0037382015 scopus 로고    scopus 로고
    • Estimating and validating the cumulative distribution of a function of random variables: Toward the development of distribution arithmetic
    • W.A. Lodwick, and K.D. Jamison Estimating and validating the cumulative distribution of a function of random variables: toward the development of distribution arithmetic Reliable Computing 9 2 2003 127 141
    • (2003) Reliable Computing , vol.9 , Issue.2 , pp. 127-141
    • Lodwick, W.A.1    Jamison, K.D.2
  • 12
    • 0348029368 scopus 로고
    • Estimates for the distribution function of a sum of two random variables when the marginal distributions are fixed
    • G.D. Makarov Estimates for the distribution function of a sum of two random variables when the marginal distributions are fixed Theory of Probability and its Applications 26 1981 803 806
    • (1981) Theory of Probability and Its Applications , vol.26 , pp. 803-806
    • Makarov, G.D.1
  • 13
    • 0037399671 scopus 로고    scopus 로고
    • Interval analysis and fuzzy set theory
    • R.E. Moore, and W.A. Lodwick Interval analysis and fuzzy set theory Fuzzy Sets and Systems 135 1 2003 5 9
    • (2003) Fuzzy Sets and Systems , vol.135 , Issue.1 , pp. 5-9
    • Moore, R.E.1    Lodwick, W.A.2
  • 14
    • 0002161065 scopus 로고    scopus 로고
    • Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications
    • R.B. Kearfott Kluwer Dordrecht*et al.
    • H.T. Nguyen, and V. Kreinovich Nested Intervals and Sets: Concepts, Relations to Fuzzy Sets, and Applications R.B. Kearfott Applications of Interval Computations 1996 Kluwer Dordrecht 245 290
    • (1996) Applications of Interval Computations , pp. 245-290
    • Nguyen, H.T.1    Kreinovich, V.2
  • 17
    • 20344393962 scopus 로고
    • How often are the observations normal?
    • A.I. Orlov How often are the observations normal? Industrial Laboratory 57 7 1991 770 772
    • (1991) Industrial Laboratory , vol.57 , Issue.7 , pp. 770-772
    • Orlov, A.I.1
  • 21
    • 0026206489 scopus 로고
    • An extreme limit theorem for dependency bounds of normalized sums of random variables
    • R.C. Williamson An extreme limit theorem for dependency bounds of normalized sums of random variables Information Sciences 56 1991 113 141
    • (1991) Information Sciences , vol.56 , pp. 113-141
    • Williamson, R.C.1
  • 22
    • 0002063018 scopus 로고
    • Probabilistic arithmetic I: Numerical methods for calculating convolutions and dependency bounds
    • R. Williamson, and T. Downs Probabilistic arithmetic I: numerical methods for calculating convolutions and dependency bounds International Journal of Approximate Reasoning 4 2 1990 89 158
    • (1990) International Journal of Approximate Reasoning , vol.4 , Issue.2 , pp. 89-158
    • Williamson, R.1    Downs, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.