A compound Poisson model for the annual area burned by forest fires in the province of Ontario

Abstract We use the compound Poisson probability distribution to model the annual area burned by forest fires in the Canadian province of Ontario. Models for sums‐of‐random variables, relevant for modeling aggregate insurance claims and assessing insurance risk are also relevant in modeling aggregate area burned based on sums of sizes of individual fires. Researchers have fit the distribution of fire sizes to the truncated power‐law (or Pareto) distribution (Ward et al ., 2001) and a four‐parameter Weibull distribution (Reed and McKelvey, 2002 ). Armstrong ( 1999 ) fitted a lognormal distribution to annual proportion of area burned by forest fires in a region of Alberta. We derive expressions and moments for aggregate area burned in Ontario using fire data from the Ontario Ministry of Natural Resources (OMNR). We derive expressions for the distribution of area burned for “severe” and “mild” fire weather scenarios and for “intensive suppression” and “no suppression” scenarios (represented by the intensive and extensive fire protection zones of the province). These distributions can be used to perform risk analysis of annual area burned. Copyright © 2009 John Wiley & Sons, Ltd.