Mixed Poisson Processes: 1st Edition (Hardback) book cover

Mixed Poisson Processes

1st Edition

By J Grandell

Chapman and Hall/CRC

280 pages

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Hardback: 9780412787003
pub: 1997-05-01
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Description

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.

Table of Contents

Preface

Introduction

The Mixed Poisson Distributions

Some Basic Concepts

The Mixed Poisson Process

Some Related Processes

Cox Processes

Gauss-Poisson Processes

Mixed Renewal Processes

Characterization of Mixed Poisson Processes

Reliability Properties of Mixed Poisson Processes

Characterization within Birth Processes

Characterization within Stationary Point Processes

Characterization within General Point Processes

Compound Mixed Poisson Distributions

Compound Distributions

Exponential Bounds

Asymptotic Behaviour

Recursive Evaluation

The Risk Business

The Claim Process

Ruin Probabilities

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis