Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/267632 
Year of Publication: 
2019
Citation: 
[Journal:] Journal of Industrial Engineering International [ISSN:] 2251-712X [Volume:] 15 [Issue:] 4 [Publisher:] Springer [Place:] Heidelberg [Year:] 2019 [Pages:] 651-665
Publisher: 
Springer, Heidelberg
Abstract: 
Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have received less attention in the literature. In this paper, we present the definition, properties, characteristics and PH representations of ADPH distributions and their subclasses with finite state space. Based on the definitions of geometric and shifted geometric distributions, we propose a distinct classification for the ADPH subclasses analogous to ACPH family. We develop the PH representation for each ADPH subclass and prove them through their closure properties. The advantage of our proposed classifications is in applying precise representations of each subclass and preventing miscalculation of the probability mass function, by computing the ADPH family based on geometric and shifted geometric distributions.
Subjects: 
Phase-type distribution
Acyclic discrete phase-type distribution (ADPH)
Classifcation of ADPH
Representations of ADPH
Geometric and shifted geometric distribution
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article

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