The paper discusses the development of several procedures for estimating parameters of statistical models, by making allowances for the errors inherent in observed data and applying this to a data set describing the South African insurance landscape. The classical assumption that the real observation is a sum of two random variables, namely the actual (true) value of the observed variable and observational error, is considered. Most often the error is assumed to be distributed as Gaussian noise; however, other distributions for the error function may sometimes offer better approximations. The paper considers the Laplacian distribution as an additional option. The approach is applied, for both assumptions as well as for other well-known methodologies, to estimate parameters of the frequency-magnitude Gutenberg-Richer relation, which describes the distribution of different sizes of earthquakes. The implications of the newly derived estimation procedures for the insurance industry are also discussed. This pertains specifically to the estimation procedures serving as a means to improve the hazard at risk for short term property reinsurance caused by earthquakes. A discussion of the probabilistic seismic risk assessment methodology and an application to the South African insurance landscape underpins the above investigation.

This paper will summarise the findings of research that is currently being conducted. In terms of the Congress, the paper will aim to discuss the statistical findings and focus on the implications for the insurance industry, particularly pertaining to short term property insurance. This is expected to be done by means of a presentation with the opportunity for discussion afterwards.

Keywords: Observation errors, parameter estimates, reinsurance, earthquake magnitudes, catastrophe insurance, probabilistic seismic risk analysis