Abstract
Different types of natural events hit the United States every year. The data of natural hazards from 1900 to 2016 in the US shows that there is an increasing trend in annul natural disaster losses after 1980. Climate change is recognized as one of the factors causing this trend, and predictive analysis of natural losses becomes important in loss prediction and risk prevention as this trend continues. In this paper, we convert natural disaster losses to the year 2016 dollars using yearly average Consumers Price Index (CPI), and conduct several tests to verify that the CPI adjusted amounts of loss from individual natural disasters are independent and identically distributed. Based on these test results, we use various model selection quantities to find the best model for the natural loss severity among three composite distributions, namely Exponential-Pareto, Inverse Gamma-Pareto, and Lognormal-Pareto. These composite distributions model piecewise small losses with high frequency and large losses with low frequency. Remarkably, we make the first attempt to derive analytical Bayesian estimate of the Lognormal-Pareto distribution based on the selected priors, and show that the Lognormal-Pareto distribution outperforms the other two composite distributions in modeling natural disaster losses. Important risk measures for natural disasters are thereafter derived and discussed.
Highlights
Different types of natural events hit the United States (US) every year
Dollars using the annual average Consumers Price Index (CPI)3. We found that both the numbers of natural events and the CPI adjusted total damages have been increasing over the time; there is no visible trend in the individual CPI adjusted losses, which is consistent with the conclusion claimed by Levi and Partrat (1991)
We propose using composite distributions to model natural disaster losses
Summary
Different types of natural events hit the United States (US) every year. The east coast of the US suffers hurricanes, the middle of the US sees tornadoes, the west coast of the US endures earthquake, and the south of the US bears a variety of issues such as hurricane, wind, drought, and floods. Levi and Partrat (1991) analyzed hurricane losses between 1954 and 1986 in the US, and found that the amounts of losses were independent and identically distributed (i.i.d.) and independent of the frequencies of hurricanes These assumptions are confirmed in our research, based on the EM-DAT natural disaster data from 1900 to 2016 after taking into account price inflations. Levi and Partrat (1991) proposed to use lognormal distribution for the losses of natural events based on the hurricane data between 1954 and 1986 in the US This distribution cannot describe the typical feature of the natural disaster losses, i.e., many small amounts of losses and occasional occurrence of huge amount of losses. The CPI data was download from Bureau of Labor Statistics https://data.bls.gov/pdq/SurveyOutputServlet
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