Effects of probability distribution choice on likelihood estimates in risk analysis

In real life risk assessment, a risk event with a likelihood of 1/100 can be easily but mistakenly estimated to have likelihood of 1/1,000, 1/10,000 or even smaller due to an inadequate probability distribution choice. Contrasting to the underestimating, an overestimating can also occur. This paper establishes a systematic and general way of evaluating these underestimating or overestimating situations. The paper applies the method to several commonly used probability distributions, namely Normal, Weibull, Log Normal, and Gumbel distributions, and draws some general conclusions and quantitative trends of overestimating or underestimating possibilities. The paper also provides some general advice for selecting a probability distribution when the sample size of data is small or the risk assessment needs to extrapolate the likelihood estimates to a tail end with no experience. With the method and quantitative trending data presented, the paper will help enhance the validity of risk likelihood estimates leading to a better risk assessment.