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 ...

This paper provides a detailed study on discrete phase type (DPH) distributions and its acyclic subclass referred to as acyclic-DPH (ADPH). Previously not considered similarities and differences between DPH and continuous phase type (CPH) distributions are investigated and minimal representations, called canonical forms, for the subclass of ADPH distributions are provided. We investigate the co...

The main goal of this paper is to derive properties about Discrete Phase Type (DPH) distributions and to provide results which make convenient their use in the approximate analysis of discrete state non-Markovian stochastic systems. To this end, similarities and di erences between DPH and Continuous Phase Type (CPH) distributions are investigated. An immediate di erence is that DPH distribution...

IV jPhaseFit: the fitting module 5 IV-A Abstract Classes . . . . . . . . . . . . . . . . . . . . . . . . . 6 IV-B Concrete Classes: Maximum Likelihood Algorithms . . . . . . . 6 IV-B.1 General Phase-Type Distribution EM Algorithm [1] . . 6 IV-B.2 Hyper-Exponential Distribution EM Algorithm [2] . . . 7 IV-B.3 Hyper-Erlang Distribution EM Algorithm [3] . . . . . 7 IV-C Concrete Classes: Moment Ma...

We are interested in proving that variable elimination (VE) in discrete Bayesian networks always yields a clearly structured conditional probability table (CPT) rather than a potential as universally stated. A Bayesian network consists of a directed acyclic graph and a corresponding set of CPTs. Based on the conditional independencies holding in the directed acyclic graph, the product of the CP...

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 computat...

In discrete event systems event times are often correlated among events of one event stream and also between different event streams. If this correlation is neglected, then resulting simulation models do not describe the real behavior in a sufficiently accurate way. In most input modeling approaches, no correlation or at most the autocorrelation of one event stream is considered, correlation be...

Finding new families of distributions has become a popular tool in statistical research. In this article, we introduce a new flexible four-parameter discrete model based on the Marshall-Olkin approach, namely, the discrete Kumaraswamy Marshall-Olkin exponential distribution. The proposed distribution can be viewed as another generalization of the geometric distribution and enfolds some importan...