Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-07T20:35:59.102Z Has data issue: false hasContentIssue false

2 - Claim-severity distribution

from Part I - Loss models

Published online by Cambridge University Press:  05 June 2012

Yiu-Kuen Tse
Affiliation:
Singapore Management University
Get access

Summary

Claim severity refers to the monetary loss of an insurance claim. Unlike claim frequency, which is a nonnegative integer-valued random variable, claim severity is usually modeled as a nonnegative continuous random variable. Depending on the definition of loss, however, it may also be modeled as a mixed distribution, i.e. a random variable consisting of probability masses at some points and continuous otherwise.

We begin this chapter with a brief review of some statistical tools for analyzing continuous distributions and mixed distributions. The use of the survival function and techniques of computing the distribution of a transformed random variable are reviewed. Some standard continuous distributions for modeling claim severity are summarized. These include the exponential, gamma, Weibull, and Pareto distributions. We discuss methods for creating new claim-severity distributions such as the mixture-distribution method. As losses that are in the extreme right-hand tail of the distribution represent big losses, we examine the right-hand tail properties of the claim-severity distributions. In particular, measures of tail weight such as limiting ratio and conditional tail expectation are discussed. When insurance loss payments are subject to coverage modifications such as deductibles, policy limits, and coinsurance, we examine their effects on the distribution of the claim severity.

Learning objectives

  1. Continuous distributions for modeling claim severity

  2. Mixed distributions

  3. Exponential, gamma, Weibull, and Pareto distributions

  4. Mixture distributions

  5. Tail weight, limiting ratio, and conditional tail expectation

  6. Coverage modification and claim-severity distribution

Review of statistics

In this section we review some results in statistical distributions relevant for analyzing claim severity.

Type
Chapter
Information
Nonlife Actuarial Models
Theory, Methods and Evaluation
, pp. 41 - 85
Publisher: Cambridge University Press
Print publication year: 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Claim-severity distribution
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.005
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Claim-severity distribution
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.005
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Claim-severity distribution
  • Yiu-Kuen Tse, Singapore Management University
  • Book: Nonlife Actuarial Models
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812156.005
Available formats
×