Probability, convolutions, and distributions: EPRI monographs on simulation of electric power production
- Ohio Univ., Athens, OH (United States). Dept. of Physics and Astronomy
Probability theory is approached analytically to derive and explain formulas of particular interest in planning and operating electric power generating systems. To do this, the convolution process for obtaining the probability distribution of the sum of random variables is discussed at length. The application in mind is forecasting production cost and reliability, taking into account random outages of generating units. A tutorial approach is taken to define empirical and formal probability and to introduce notation and terminology for describing probability distributions. Distribution parameters, properties, generating functions and use of cumulants instead of moments are presented. The theory or orthogonal function expansions and their application to probability problems is developed, starting with Fourier series and proceeding to novel perspectives. Gram-Charlier Type A Series, Hermite polynomials, Edgeworth expansion, Cornish-Fisher formulas and Laguerre polynomial expansions are analyzed and exemplified. The text includes illustrative exercises, a review of the literature and a bibliography of 138 references.
- Research Organization:
- Electric Power Research Inst., Palo Alto, CA (United States); Ohio Univ., Athens, OH (United States). Dept. of Physics and Astronomy
- Sponsoring Organization:
- EPRI; Electric Power Research Inst., Palo Alto, CA (United States)
- OSTI ID:
- 5369132
- Report Number(s):
- EPRI-IE-7508
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
240100* -- Power Systems-- (1990-)
661300 -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
DISTRIBUTION FUNCTIONS
ELECTRIC POWER
FORECASTING
FOURIER ANALYSIS
FUNCTIONS
HERMITE POLYNOMIALS
INTEGRAL TRANSFORMATIONS
LAGUERRE POLYNOMIALS
MATHEMATICS
OPERATION
POLYNOMIALS
POWER
POWER SYSTEMS
PROBABILITY
SERIES EXPANSION
TRANSFORMATIONS