Factors Affecting Fire Loss—Multiple Regression Models with Extreme Values

In his paper to the Tenth ASTIN Colloquium the author presented generalised extreme value techniques for making use of all large losses that are available for analysis and not merely the largest. In this paper the problem of assessing the relative contributions of various factors to fire losses is investigated. A model concerned with multiple regression with extreme observations of given rank is developed. It takes into consideration the biases due to the use of extremes and the differences between categories of risks in regard to the frequency of fires (or claims). By way of illustration the model was applied to the largest and second largest losses in the textile industries in the United Kingdom during the six-year period 1965 to 1970. The presence or absence of sprinklers, whether the buildings were single-storey or multi-storey, and total floor area were the independent variables included in this preliminary investigation. Judged from extreme losses sprinklers appear to reduce considerably the expected damage in all fires. The technique enables different estimates to be obtained for each regression parameter for different ranks. It is desirable to have a single overall estimate for each parameter; and for this purpose a second model is developed for performing a regression analysis combining observations pertaining to a number of ranks. Covariances of the residual errors are also taken into account in this model.