ISSN:
1572-9443
Keywords:
Approximation
;
convergence in distribution
;
denseness, Erlang distribution
;
generalized hyperexponential distribution
;
method of stages
;
weak convergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract Generalized hyperexponential (GH) distributions are linear combinations of exponential CDFs with mixing parameters (positive and negative) that sum to unity. The denseness of the class GH with respect to the class of all CDFs defined on [0, ∞) is established by showing that a GH distribution can be found that is as close to a given CDF as desired, with respect to a suitably defined metric. The metric induces the usual topology of weak convergence so that, equivalently, there exists a sequence of GH CDFs that converges weakly to a given CDF. This result is established by using a similar result for weak convergence of Erlang mixtures. Various set inclusion relations are also obtained relating the GH distributions to other commonly used classes of approximating distributions, including generalized Erlang (GE), mixed generalized Erlang (MGE), those with reciprocal polynomial Laplace transforms (K n ), those with rational Laplace transforms (R n ), and phase-type (PH) distributions. A brief survey of the history and use of approximating distributions in queueing theory is also included.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01536187
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