Mixed Poisson Processes

1. Auflage 1997
ISBN: 978-0-412-78700-3
Verlag: Science Publishers

Buch, Englisch, 280 Seiten, Format (B × H): 138 mm x 216 mm, Gewicht: 453 g

Reihe: Chapman & Hall/CRC Monographs on Statistics and Applied Probability

To date, Mixed Poisson processes have been studied by scientists primarily interested in either insurance mathematics or point processes. Work in one area has often been carried out without knowledge of the other area. Mixed Poisson Processes is the first book to combine and concentrate on these two themes, and to distinguish between the notions of distributions and processes. The first part of the text gives special emphasis to the estimation of the underlying intensity, thinning, infinite divisibility, and reliability properties. The second part is, to a greater extent, based on Lundberg's thesis.

Zielgruppe

Professional

Autoren/Hrsg.

Grandell, J

Fachgebiete

• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Preface -- 1 Introduction -- 2 The mixed Poisson distribution -- 3 Some basic concepts -- 4 The mixed Poisson process -- 5 Some related processes -- 5.1 Cox processes -- 5.2 Gauss-Poisson processes -- 5.3 Mixed renewal processes -- 6 Characterization of mixed Poisson processes -- 6.1 Characterization within birth processes -- 6.2 Characterization within stationary point processes -- 6.3 Characterization within general point processes -- 7 Reliability properties of mixed Poisson processes -- 8 Compound mixed Poisson distributions -- 8.1 Compound distributions -- 8.2 Exponential bounds -- 8.3 Asymptotic behaviour -- 8.4 Recursive evaluation -- 9 The risk business -- 9.1 The claim process -- 9.2 Ruin probabilities -- References and author index -- List of notation -- Subject index.

Über Autor(innen)

Jan Crandall is Professor of Mathematical Statistics in the Department of Mathematics at the Royal Institute of Technology, Stockholm, Sweden.