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Likelihood estimation for generalized mixed exponential distributions
Author(s) -
Harris Carl M.,
Sykes Edward A.
Publication year - 1987
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198704)34:2<251::aid-nav3220340210>3.0.co;2-k
Subject(s) - mathematics , exponential function , exponential family , convergence (economics) , class (philosophy) , mathematical optimization , set (abstract data type) , regular polygon , computer science , mathematical analysis , artificial intelligence , economics , programming language , economic growth , geometry
The class of functions expressed as linear (not necessarily convex) combinations of negative exponential functions is dense in the set of all square integrable functions on the nonnegative reals. Because of this and resultant mathematical properties, linear combinations of exponential densities have excellent potential for wide application in stochastic modeling. This work documents the development and testing of a practical procedure for maximum‐likelihood estimation for these generalized exponential mixtures. The algorithm offered for the problem is of the Jacobi type and guarantees that the result will provide a legitimate probability function of the prescribed type. Extensive testing has been performed and results are very favorable: convergence is rapid and the use of computer resources rather limited.