The Lognormal Model for the Distribution of one Claim

Abstract

The most important property of a distribution function to be used as a model for the distribution of one claim is of course that it fits the data well enough. If there is no natural truncation point in the data a more formal demand is that all the moments of the distribution function exist. Further, to be of a real value to the statistician, the chosen d.f. ought to be reasonably handy to use. As all the moments of the lognormal d.f. exist the first point to be checked is whether the lognormal d.f. fits the data. The other points on the list below are the qualities that I think are of the greatest value when using a distribution function, i.e. they reflect the handiness of the d.f.Does the lognormal d.f.1. Fit the data?2. Give an unbiased and efficient estimate of the mean? It is important that this estimate is not too difficult to compute.3. Give a practicable confidence interval of the mean?4. Give a known distribution function of the estimate of the risk premium?This paper is an attempt to give an affirmative answer to these questions. As the lognormal distribution function has been treated in the monograph “The lognormal distribution” by J. Aitchison and J. A. C. Brown (Cambridge University Press) the theory of this distribution function will not be dealt with more than necessary for the context.