The Use of Coxian Phase-Type Distribution To Model the University Student Progression and Drop out Rates: The Case of a Italian University
Adele H. Marshall2, Mariangela Zenga1, Filippo Domma3, Sabrina Giordano3
1Metodi Quantitativi per le Scienze Economiche ed Aziendali, Università Milano-Bicocca, Milano, Italy; 2Centre for Statistical Science and Operational Research (CenSSOR), Queen's University of Belfast, Belfast, Northern Ireland, United Kingdom; 3Department of Economics and Statistics, University of Calabria, Arcavacata di Rende, Cosenza, Italy

The student time at university is consisting of different phases or stages in the student status from the enrollment to the different exits. The Coxian phase-type distributions are used to model such a system whereby the student is a unit in the system that moves along sequential stages until they complete their degree or drop out of their course and leave the system completely. The Coxian phase-type distribution models the time to absorption of a finite Markov chain whereby the system is considered to consist of a series of ordered phases by which the process begins in the first phase and may either progress through the phases sequentially or enter into the absorbing state (the terminating event). Such phases may then be used to describe stages of a process which terminates at some stage.The Coxian phase-type model is used to represent the time taken for some cohorts of students to complete their degree or to leave before completing their studies in a italian university. As a result, it is possible to consider students as leaving university at different phases/stages of time at university whereby each phase is assigned a reasonable meaning.Moreover, the analysis is also concerned with investigating and thus verifying the effects of some covariates and their use in partitioning the units into the various phases and the corresponding transition probabilities.


1. M. Faddy, Examples of fitting structured phase-type distribution, Applied Stochastic models and Data Analysis,10,pag 247-255

2. Smith J.P., Robin A.N., (2001) Dropping out of university: a statistical analysis of the probability of withdrawal for UK university students Journal of the Royal Statistical Society. Series A Vol. 164, Part 2, pag 389-405.

Keywords: Coxian Phase type Distribution; Survival analysis; Italian educational system; Students carriers

Biography: Assistant professor in Social Statistics at the Milano-Bicocca University.

Interested in: survival analysis for socio-demographic phenomena, classification tree.