Chapter 5. Models for the number of losses: Counting distributions

  1. Harry H. Panjer

Published Online: 6 MAR 2006

DOI: 10.1002/0470051310.ch5

Operational Risk: Modeling Analytics

Operational Risk: Modeling Analytics

How to Cite

Panjer, H. H. (2006) Models for the number of losses: Counting distributions, in Operational Risk: Modeling Analytics, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0470051310.ch5

Publication History

  1. Published Online: 6 MAR 2006
  2. Published Print: 25 AUG 2006

ISBN Information

Print ISBN: 9780471760894

Online ISBN: 9780470051313



  • compounding;
  • zero-truncated;
  • Neyman Type A;
  • additive exponential dispersion family (AEDF);
  • reproductive exponential disperison family (REDF)


This chapter contains sections titled:

  • Introduction

  • The Poisson Distribution

  • The Negative Binomial Distribution

  • The Binomial Distribution

  • The (a, b, 0) Class

  • The (a, b, 1) Class

  • Compound Frequency Models

  • Recursive Calculation of Compound Probabilities

  • An Inventory of Discrete Distributions

  • A Hierarchy of Discrete Distributions

  • Further Properties of the Compound Poisson Class

  • Mixed Frequency Models

  • Poisson Mixtures

  • Effect of Exposure on Loss Counts

  • TVaR for Discrete Distributions

  • Exercises