ABSTRACT
S0REN ASMUSSEN Department of Mathematical Statistics , Lund University, Box 1 18 , S-221 00 Lund, Sweden
1 INTRODUCTION
This paper is concerned with statistical aspects of Markovian modeling: how do we fit a phase-type (PHT) distribution or a point process with a Markovian structure (MPP) to a given set of data? The need for developing methods in this area is obvious . PHT distributions and MPP's have by now attained widespread in the modeling of queues (e .g . Neuts , 198 1 , Sengupta, 1989) , insurance risk processes (e .g . Asmussen & Rolski, 1991 ) , renewal theory (e .g . Neuts, 1978 , Kao , 1988, Lipsky, 1992, Asmussen & Bladt , 1995) , reliability (e .g . Bobbio et at. , 1980, Jonsson et at. , 1994) and many other areas (for an extensive list of recent references , see Neuts , 1995) . By using this type of models, the
stochasticprocessunderstudybecomesMarkovianwhichcanbeexploitedinvariousways toderiveanalgorithmictractablesolutioninmanycaseswhereexponentialdistributions /Poissonprocesseshaveearlierappearedtobetheonlyfeasibleassumptions .Further, inviewofdensenessresultslikethoseofSchassberger( 1973) ,Asmussen&Koole( 1993) , basicallyanyoftheprocessesintheareaswehavementionedcanbeapproximatedbya model having such Markovian structure.
