Non-homogeneous Poisson process - estimation and simulation

• Thesis title in Czech: Nehomogenní Poissonův proces - odhadování a simulace
• Thesis title in English: Non-homogeneous Poisson process - estimation and simulation
• Key words: Poissonův proces, nehomogenní, odhadování, funkce intenzity, simulace
• English key words: Poisson process, non-homogeneous, inhomogeneous, estimation, intensity function, simulation
• Academic year of topic announcement: 2016/2017
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Department of Probability and Mathematical Statistics (32-KPMS)
• Supervisor: doc. RNDr. Michal Pešta, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 17.02.2017
• Date of assignment: 17.02.2017
• Confirmed by Study dept. on: 28.02.2017
• Date and time of defence: 05.09.2018 08:00
• Date of electronic submission: 19.07.2018
• Date of submission of printed version: 20.07.2018
• Date of proceeded defence: 05.09.2018
• Opponents: doc. RNDr. Zbyněk Pawlas, Ph.D.

Guidelines

The thesis will cover discussion about properties of the non-homogeneous Poisson process together with estimation of its intensity function having parametric form. Furthermore, simulation approaches of the non-homogeneous Poisson process will be described from a theoretical perspective. The summarized theoretical methods will be applied on real data from non-life insurance.

References

P. Bratley, B. L. Fox, and L. E. Schrage. A Guide to Simulation. Springer-Verlag, New York, 1987.
R. W. Klein and S. D. Roberts. A time-varying Poisson arrival process generator. Simulation, 43(4):193–195, 1984.
M. E. Kuhl and J. R. Wilson. User’s manual for mp3mle and mp3sim: software for estimating and simulating nonhomogeneous Poisson processes. Technical report, North Carolina State University, Department of Industrial Engineering, 1996.
S. H. Lee, M. M. Crawford, and J. R. Wilson. Modeling and simulation of a nonhomogeneous Poisson process having cyclic behavior. Communications in Statistics — Simulation, 20(2 & 3):777–809, 1991.
P. A. W. Lewis and G. S. Shedler. Simulation of nonhomogenous Poisson processes with log-linear rate function. Biometrika, 63:501–505, 1976.
P. A. W. Lewis and G. S. Shedler. Simulation of nonhomogenous Poisson processes by thinning. Naval Research Logistics Quarterly, 26(3):403–413, 1979.
P. A. W. Lewis and G. S. Shedler. Simulation of nonhomogenous Poisson processes with degree-two exponential polynomial rate function. Operations Research, 27(5):1026–1039, 1979.