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Multistage Curve Fitting

Published online by Cambridge University Press:  29 August 2014

Christoph Haehling von Lanzenauer  and
Don Wright
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One of the most important properties of a distribution function is that it fits the data well enough for the decision-makers' or analysts' purposes. The statisticians' problem is to select a specific form for the distribution function and to determine its parameters from the available data. Various methods (graphical method, method of moments, maximum likelihood method) are available for that purpose.

In many real world situations a single distribution function, however, may not be appropriate over the entire range of the available data. This suggests that the underlying process changes over the range of the respective variable. This fact should be considered in curve fitting. A typical example of such a situation is given in Figure 1 representing third party liability losses for trucks.

It is interesting to speculate about the different raisons d'être (Seal [5]) for the observed discontinuity. It may be the result of out-of-court or in-court settlements or could stem from differences between bodily injury and property damages.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 9 , Issue 1-2 , January 1977 , pp. 191 - 202
Copyright
Copyright © International Actuarial Association 1977

References

[1]Almer, B., Risk Analysis in Theory and Practical Statistics, Trans. XV International Congress of Actuarıes, New York, 1957, 2, pp. 314–349.Google Scholar
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[5]Seal, H., Stochastıc Theory of a Risk Business, Wiley, 1969.Google Scholar
[6]Wilde, D., Optimum Seeking Methods, Prentice Hall, 1964.Google Scholar