NMAK15019U Phase-type distributions: Theory and applications (AAM)
MSc programme in Actuarial Mathematics
MSc programme in Statistics
This course deals with stochastic modelling with examples from insurance risk, queueing theory and reliability theory. Necessary tools from renewal theory, random walks and Markov processes are introduced. In particular ladder height methods and Wiener–hopf techniques will be of importance.
The class of phase–type (PH) distributions, defined as the distribution of a first exit time from a transient set of a Markov jump process, will play an important role in the course. Included in the class PH are convolutions and mixtures of exponential distributions. The class of PH distributions is dense in the class of distributions on the positive reals, and the PH assumption will in many cases provide exact, even explicit, solutions to many complex stochastic models.
This is for example the case in renewal theory, ladder height distributions, ruin probabilities, the severity of ruin, or some waiting time distributions in queues, where we obtain explicit formulas. In reliability theory, the PH distributions naturally describe the distribution of lifetimes which may be seen to go through different stages prior to failure.
The assumption of PH distributions being involved enables us to use probabilistic reasoning, which is a powerful technique that often avoids tedious calculations, and in some cases provides solutions which cannot readily be obtained by analytic methods. A probabilistic method uses sample path arguments rather than transition probabilities or transform methods, which would be the preferred methods in an analytic approach.
At the end of the course the student is expected to have:
Knowledge about renewal theory, random walks, Markov processes, phase-type distributions, ladder height distributions, ruin probabilities, severity of ruin, waiting time distributions in queues, lifetime distributions in reliability theory.
Skills to formalize phase-type distributions, discuss their theoretical background, and apply them in insurance theory, queueing theory and reliability theory.
Competences in the contents of the course.
- Category
- Hours
- Lectures
- 28
- Preparation
- 178
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutesExamination without preparation
- Aid
- Without aids
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK15019U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- B
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Mogens Steffensen (6-74766e6c757a4774687b6f35727c356b72)
Lecturers
Mogens Bladt