Effective Minimization of Acyclic Phase-Type Representations

Acyclic phase-type distributions are phase-type distributions with triangular matrix representations. They constitute a versatile modelling tool, since they (1) can serve as approximations to any continuous distributions, and (2) exhibit special properties and characteristics, which usually result in some ease in analysis. The size of the matrix representation has a strong influence on computational efforts needed when analyzing these distributions. This representation, however, is not unique, and two representations of the same distribution can differ drastically in size. This paper proposes an effective procedure to aggregate the size of the matrix representation without altering the distribution.

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