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Likelihood estimation for generalized mixed exponential distributions

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  • Carl M. Harris
  • Edward A. Sykes

Abstract

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.

Suggested Citation

  • Carl M. Harris & Edward A. Sykes, 1987. "Likelihood estimation for generalized mixed exponential distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 251-279, April.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:2:p:251-279
    DOI: 10.1002/1520-6750(198704)34:23.0.CO;2-K
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    Cited by:

    1. Carl M. Harris & William G. Marchal, 1998. "Distribution Estimation Using Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 10(4), pages 448-458, November.

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