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10 - Statistical distributions

Published online by Cambridge University Press:  07 October 2011

Paul Sweeting
Affiliation:
University of Kent, Canterbury
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Summary

Univariate discrete distributions

The univariate statistical distribution of each variable on its own – also known as its marginal distribution – is an important factor in the risk it poses. Many of the features above can be modelled directly by the appropriate choice of marginal distribution, or they can be added to a more ‘basic’ marginal distribution.

Univariate discrete distributions are generally only used when the number of observations is small, as they quickly become difficult to deal with as the numbers involved increase. However, even if continuous approximations are used, it is important to recognise the nature of whatever is being approximated.

The binomial and negative binomial distributions

The binomial distribution is fundamental to many risks faced. In particular, it reflects the risk of a binary event – one which may or may not occur. Such an event could be the payment of a claim, the default of a creditor or the survival of a policyholder.

The binomial distribution is parameterised by the number of trials (or observations), n, the number of successes (or claims, defaults or other events), x, and the probability that an event will occur, p. The probability must be constant for each trial.

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Publisher: Cambridge University Press
Print publication year: 2011

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  • Statistical distributions
  • Paul Sweeting, University of Kent, Canterbury
  • Book: Financial Enterprise Risk Management
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511844133.011
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  • Statistical distributions
  • Paul Sweeting, University of Kent, Canterbury
  • Book: Financial Enterprise Risk Management
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511844133.011
Available formats
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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.

  • Statistical distributions
  • Paul Sweeting, University of Kent, Canterbury
  • Book: Financial Enterprise Risk Management
  • Online publication: 07 October 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9780511844133.011
Available formats
×