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Flowgraph Models for Generalized Phase Type Distributions Having Non‐Exponential Waiting Times
Author(s) -
Huzurbazar Aparna V.
Publication year - 1999
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00142
Subject(s) - phase type distribution , mathematics , generalization , exponential function , markov chain , exponential distribution , type (biology) , markov process , exponential type , markov model , property (philosophy) , markov renewal process , markov property , mathematical optimization , statistics , mathematical analysis , ecology , philosophy , epistemology , biology
. Aalen (1995) introduced phase type distributions based on Markov processes for modelling disease progression in survival analysis. For tractability and to maintain the Markov property, these use exponential waiting times for transitions between states. This article extends the work of Aalen (1995) by generalizing these models to semi‐Markov processes with non‐exponential waiting times. The generalization allows more realistic modelling of the stages of a disease where the Markov property and exponential waiting times may not hold. Flowgraph models are introduced to provide a closed form for the distributions in situations involving non‐exponential waiting times. Flowgraph models work where traditional methods of stochastic processes are intractable. Saddlepoint approximations are used in the analysis. Together, generalized phase type distributions, flowgraphs, and saddlepoint approximations create exciting and innovative prospects for the analysis of survival data.