frequency-severity decomposition

Imagine you run a car insurance book and you want to know how much you will pay out next year. Trying to guess the single number 'total claims' directly is hard. It is much easier to ask two simpler questions: how many accidents will happen, and how big will each one be? Frequency-severity decomposition is exactly this habit of splitting the cost of claims into a count part and a size part.

Frequency is the number of claims (how often), and severity is the amount of each claim (how much). The everyday link is: expected total cost is roughly expected number of claims multiplied by expected size of a claim. For example, if a policy has on average 0.10 claims per year and the average claim is 3,000, the expected annual cost is about 0.10 times 3,000 = 300. Modelling them separately lets an actuary use a count distribution (like Poisson) for frequency and a positive-amount distribution (like lognormal or Pareto) for severity, then recombine them.

This split is the backbone of non-life (property and casualty) pricing and reserving. It matters because the two pieces behave differently and respond to different forces: frequency may fall when roads get safer or anti-theft devices improve, while severity may climb with inflation, medical costs, or larger court awards. Keeping them apart also makes policy features easy to model — a deductible mostly cuts frequency and trims severity, while a policy limit only caps severity. A common pitfall is assuming frequency and severity are independent; sometimes they are linked (bad winters bring both more crashes and worse crashes), and a careful analyst checks rather than assumes.