User:Helgus/ Theory of random events (Crisp mathematical eventology)

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Theory of random events (crisp mathematical eventology) is a mathematical language of eventology – a new direction the probability theory; is based on the principle of eventological duality of notion of a set of random events and a random set of events; studying eventological distributions of a set of random events and eventological structures of its dependencies.


The basic eventological terms[edit]

  • Event, probability and value
  • Conditional event, conditional probability and conditional value
  • Set of events and random set of events
  • Event-terrace
  • Eventological duality
  • Eventological distribution
  • Eventological language
  • Eventological glossary
  • Additive set-functions and measures
  • Set-formulae of Mobius inversing events-terraces
  • Formulae of Mobius inversing eventological distributions
  • Set-means characteristics of a random set of events
  • Eventological Bayes's theorem
  • Frechet's covariances and correlations
  • The structure of dependencies of a set of events
  • Eventological copula

References[edit]

  • ^ Blyth C.R. (1972) On Simpson's Paradox and the Sure --- Thing Principle. - Journal of the American Statistical Association, June, 67, P.367-381.
  • ^ Dubois D., H.Prade (1988) Possibility theory. - New York: Plenum Press.
  • Feynman R.P. (1982) Simulating physics with computers. - International Journal of Theoretical Physics, Vol. 21, nos. 6/7, 467-488.
  • ^ Fr'echet M. (1935) G'en'eralisations du th'eor'eme des probabilit'es totales - Fundamenta Mathematica. - 25.
  • Hajek, Alan (2003) Interpretations of Probability. - The Stanford Encyclopedia of Philosophy (Summer 2003 Edition), Edward N.Zalta (ed.)
  • ^ Herrnstein R.J. (1961) Relative and Absolute strength of Response as a Function of Frequency of Reinforcement. - Journal of the Experimental Analysis of Behavior, 4, 267-272.
  • ^ Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decisios under risk. - Econometrica, 47, 313-327.
  • ^ Lefebvre V.A. (2001) Algebra of conscience. - Kluwer Academic Publishers. Dordrecht, Boston, London.
  • ^ Markowitz Harry (1952) Portfolio Selection. - The Journal of Finance. Vol. VII, No. 1, March, 77-91.
  • ^ Marshall Alfred A collection of Marshall's published works
  • ^ Nelsen R.B. (1999) An Introduction to Copulas. - Lecture Notes in Statistics, Springer-Verlag, New York, v.139.
  • ^ Russell Bertrand (1945) A History of Western Philosophy and Its Connection with Political and Social Circumstances from the Earliest Times to the Present Day, New York: Simon and Schuster.
  • ^ Russell Bertrand (1948) Human Knowledge: Its Scope and Limits, London: George Allen & Unwin.
  • Schrodinger Erwin (1959) Mind and Matter. - Cambridge, at the University Press.
  • ^ Shafer G. (1976). A Mathematical Theory of Evidence. – Princeton University Press.
  • ^ Smith Vernon (2002) Nobel Lecture.
  • ^ Stoyan D., and H. Stoyan (1994) Fractals, Random Shapes and Point Fields. - Chichester: John Wiley & Sons.
  • ^ Tversky A., Kahneman D. (1992) Advances in prospect theory: cumulative representation of uncertainty. - Journal of Risk and Uncertainty, 5, 297-323.
  • ^ Vickrey William Paper on the history of Vickrey auctions in stamp collecting
  • ^ Zadeh L.A. (1965) Fuzzy Sets. - Information and Control. - Vol.8. - P.338-353.
  • ^ Zadeh L.A. (1968) Probability Measures of Fuzzy Events. - Journal of Mathematical Analysis and Applications. - Vol.10. - P.421-427.
  • ^ Zadeh L.A. (1978). Fuzzy Sets as a Basis for a Theory of Possibility. – Fuzzy Sets and Systems. - Vol.1. - P.3-28.
  • ^ Zadeh L.A. (2005). Toward a Generalized Theory of Uncertainty (GTU) - An Outline. - Information sciences (to appear).
  • ^ Zadeh L.A. (2005). Toward a computational theory of precisiation of meaning based on fuzzy logic - the concept of cointensive precisiation. - Proceedings of IFSA-2005 World Congress.} - Beijing: Tsinghua University Press, Springer.


See also[edit]