Classification and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions

Acyclic Discrete Phase Type Distributions: Part 1: Properties and Canonical Forms

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...

Acyclic discrete phase type distributions: properties and a parameter estimation algorithm

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...

Acyclic Discrete Phase Type Distributions: Properties and a Parameter Estimation Algorithm

Geometric phase distributions for open quantum systems.

In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the environment and its coupling with the system yields a unique geometric phase distribution that applies even for mixed states, nonunitary dynamics, and noncyclic evo...

On Classification of Bivariate Distributions Based on Mutual Information

Among all measures of independence between random variables, mutual information is the only one that is based on information theory. Mutual information takes into account of all kinds of dependencies between variables, i.e., both the linear and non-linear dependencies. In this paper we have classified some well-known bivariate distributions into two classes of distributions based on their mutua...

On discrete a-unimodal and a-monotone distributions

Unimodality is one of the building structures of distributions that like skewness, kurtosis and symmetry is visible in the shape of a function. Comparing two different distributions, can be a very difficult task. But if both the distributions are of the same types, for example both are unimodal, for comparison we may just compare the modes, dispersions and skewness. So, the concept of unimodali...