jPhase User’s Guide Juan F. P´ erez Germ´ an Ria˜ no fern-per@uniandes.edu.co griano@uniandes.edu.co Centro de Optimizaci´on y Probabilidad Aplicada (COPA) Departamento de Ingenier´ ıa Industrial Universidad de los Andes Bogot´ a, Colombia Contents 1 Phase-Type Distributions 2 1.1 Continuous Phase-Type Distributions .......................... 2 1.2 Discrete Phase-Type Distributions ............................ 3 1.3 Closure Properties ..................................... 4 1.4 Further Closure Properties for Continuous Distributions ................ 5 1.5 Phase-Type Random Variates Generation ........................ 6 1.6 Fitting Algorithms ..................................... 6 2 jPhase: the object-oriented Framework 6 2.1 General Structure ...................................... 6 2.2 Interfaces .......................................... 7 2.3 Abstract Classes ...................................... 8 2.4 Implementing Classes ................................... 8 2.5 jPhase Examples ...................................... 8 3 jPhaseGenerator: the variates generator Module 12 3.1 PhaseGenerator Interface ................................. 12 3.2 Implementing Classes ................................... 13 3.3 jPhaseGenerator Example ............................... 13 4 jPhaseFit: the fitting module 15 4.1 Abstract Classes ...................................... 15 4.2 Maximum Likelihood Algorithms ............................. 16 4.2.1 General PH Distribution EM Algorithm ..................... 16 4.2.2 Hyper-exponential Distribution EM Algorithm ................. 16 4.2.3 Hyper-Erlang Distribution EM Algorithm .................... 16 4.3 Moment Matching Algorithms ............................... 17 4.3.1 Acyclic Continuous order-2 Distributions .................... 17 4.3.2 Erlang-Coxian Distributions ............................ 17 4.3.3 Acyclic Continuous Distributions ......................... 17 1