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A semi-infinite programming approach to identifying matrix-exponential distributions

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  • Mark Fackrell

Abstract

The Laplace–Stieltjes transform of a matrix-exponential (ME) distribution is a rational function where at least one of its poles of maximal real part is real and negative. The coefficients of the numerator polynomial, however, are more difficult to characterise. It is known that they are contained in a bounded convex set that is the intersection of an uncountably infinite number of linear half-spaces. In order to determine whether a given vector of numerator coefficients is contained in this set (i.e. the vector corresponds to an ME distribution) we present a semi-infinite programming algorithm that minimises a convex distance function over the set. In addition, in the event that the given vector does not correspond to an ME distribution, the algorithm returns a closest vector which does correspond to one.

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  • Mark Fackrell, 2012. "A semi-infinite programming approach to identifying matrix-exponential distributions," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(9), pages 1623-1631.
    • Handle: RePEc:taf:tsysxx:v:43:y:2012:i:9:p:1623-1631
    DOI: 10.1080/00207721.2010.549582
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    Cited by:

    1. A. Auslender & A. Ferrer & M. Goberna & M. López, 2015. "Comparative study of RPSALG algorithm for convex semi-infinite programming," Computational Optimization and Applications, Springer, vol. 60(1), pages 59-87, January.
    2. Belén García-Mora & Cristina Santamaría & Gregorio Rubio, 2020. "A Phase-Type Distribution for the Sum of Two Concatenated Markov Processes Application to the Analysis Survival in Bladder Cancer," Mathematics, MDPI, vol. 8(12), pages 1-15, November.

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