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Fitting combinations of exponentials to probability distributions
Author(s) -
Dufresne Daniel
Publication year - 2006
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.635
Subject(s) - log normal distribution , mathematics , exponential function , distribution (mathematics) , degenerate energy levels , polynomial , pareto principle , probability distribution , exponential distribution , statistics , mathematical analysis , physics , quantum mechanics
Two techniques are described for approximating distributions on the positive half‐line by combinations of exponentials. One is based on Jacobi polynomial expansions, and the other on the logbeta distribution. The techniques are applied to some well‐known distributions (degenerate, uniform, Pareto, lognormal and others). In theory, the techniques yield sequences of combination of exponentials that always converge to the true distribution, but their numerical performance depends on the particular distribution being approximated. An error bound is given in the case the logbeta approximations. Copyright © 2006 John Wiley & Sons, Ltd.