In this paper, a multiple regression model with extreme observations is
developed and illustrated with an example. The classical model needs to be
modified to take into consideration the biases due to the use of large values
rather than values covering the entire range of the fire loss variable. The
presence or absence of sprinklers and the height of the building, i.e. single
storey or multi-storey, are the two qualitative factors studied in this note.
The total floor area is the third independent variable included in the analysis
which is of a quantitative character. Judged from extreme losses, sprinklers
appear to reduce the expected damage considerably.
The model uses extreme observations individually; regression parameters
are estimated from two sets of extremes, viz. the largest and the second largest
and their replicated values over six years. The parameters have different
values depending upon the rank of the extremes. In a later study it is hoped
to estimate a single (constant) value for each regression parameter by carrying
out a more complicated analysis combining the information on all large losses.
