Research Article Open Access

COMPLEX PROBABILITY THEORY AND PROGNOSTIC

Abdo Abou Jaoude1
  • 1 Notre Dame University, Lebanon

Abstract

The Kolmogorov’s system of axioms can be extended to encompass the imaginary set of numbers and this by adding to the original five axioms an additional three axioms. Hence, any experiment can thus be executed in what is now the complex set C (Real set R with real probability + Imaginary set M with imaginary probability). The objective here is to evaluate the complex probabilities by considering supplementary new imaginary dimensions to the event occurring in the "real" laboratory. Whatever the probability distribution of the input random variable in R is, the corresponding probability in the whole set C is always one, so the outcome of the random experiment in C can be predicted totally. The result indicates that chance and luck in R is replaced now by total determinism in C. This new complex probability model will be applied to the concepts of degradation and the Remaining Useful Lifetime (RUL), thus to the field of prognostic.

Journal of Mathematics and Statistics
Volume 10 No. 1, 2014, 1-24

DOI: https://doi.org/10.3844/jmssp.2014.1.24

Submitted On: 27 August 2013 Published On: 9 December 2013

How to Cite: Jaoude, A. A. (2014). COMPLEX PROBABILITY THEORY AND PROGNOSTIC. Journal of Mathematics and Statistics, 10(1), 1-24. https://doi.org/10.3844/jmssp.2014.1.24

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Keywords

  • Complex Probability
  • Probability Distributions
  • Prognostic
  • Degradation
  • Lifetime