We're Skewed—The Bias in Small Samples from Skewed Distributions

People in insurance work all the time with financial processes that are best modeled with skewed distributions. Despite our constant exposure to skewed distributions, I believe when we study sample averages from these skewed distributions we think and work with them as if they were samples from normal symmetrical distributions. In this paper I want to discuss the idea that a sample average is biased lower than the actual mean of a skewed distribution – an amount that depends on the sample size and how skewed the distribution is. I will talk about the implications that this small sample bias has for credibility procedures. Why do people ignore outliers? I will offer up some possible reason for why we ignore outliers and why deals get done despite what the data indicates. I will talk about the winner's curse or why we lose even as we win. Finally, I will offer a small sample of skewed random thoughts on why these ideas explain everything from people engaging in risky behaviors to the property/casualty insurance cycle.