Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-27T04:48:10.621Z Has data issue: false hasContentIssue false

The n-Fold Convolution of a Mixed Density and Mass Function*,**

Published online by Cambridge University Press:  29 August 2014

Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The distribution of the sum of n mutuality independent random variables with a common distribution f(x) plays an important role in many insurance problems. The paper presents alternative methods of deriving the distribution of the sum of n random variables when f(x) is a mixed density and mass function. The methods are illustrated and compared.

Type
Research Article
Copyright
Copyright © International Actuarial Association 1974

Footnotes

*

This paper has been supported by a grant from the Richard Ivey Foundation.

**

The authors wish to acknowledge the helpful comments and suggestions made by Dr. P. A. Fraser, Department of Applied Mathematics, University of Western Ontario.

References

[1]Abromowitz, M and Stegun, I A (Edts), Handbook of Mathematical Functions, Dover Publications Inc, New York, 1965Google Scholar
[2]Geary, R C and Pearson, E S, Tests of Normality, London Biometrica Office, University College, 1936Google Scholar
[3]Feller, W, An introduction to Probability Theory and its Applications, Vol I and II, John Wiley & Sons, New York, 1957 and 1966Google Scholar
[4]Haehling von Lanzenauer, C., Optimal Insurance Purchasing Decisions, Working Paper Series No. 72, School of Business Administration, University of Western Ontario, 1972.Google Scholar
[5]Lighthill, M. J., Introduction to Fourier Analysis and Generalized Functions, Cambridge University Press, 1958.CrossRefGoogle Scholar
[6]Pearson, K., Tables of the Incomplete Beta-Function, Cambridge University Press, 1968.Google Scholar
[7]Seal, H., Stochastic Theory of a Risk Business, John Wiley & Sons, New York, 1969.Google Scholar
[8]Smith, V., Optimal Insurance Coverage, Journal of Political Economy, Vol 76, No. 1, 1968.CrossRefGoogle Scholar
[9]Wilks, S. S., Mathematical Statistics, John Wiley & Sons, New York, 1962.Google Scholar