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How Verisk actuaries found a use for a decades-old data distribution

Actuaries know there are many, many kinds of distributions, all with different applications. Linguists often use the Zipf-Mandelbrot (“Z-M”) Law to measure how often a word appears in a body of text. (“The” tends to be the most common word.) City planners also use it to measure city population, but it’s rarely been used in insurance—until now.

Insurers typically tend to underestimate the likelihood of a large number of claims occurring on a given policy. A more accurate estimate could help insurers, especially those pricing large policies or working on large accounts, price even more accurately. This serves as a focal point for Verisk’s latest research.

Z M Distribution

At Verisk, we’re always doing research to help you make your pricing better.

How the Z-M distribution can help insurers

In a recent study that was published in the Casualty Actuarial Society E-Forum, Verisk actuaries attempted to apply the Z-M distribution to insurance to see how it could help describe the behavior of claim frequencies. The team found situations where the Z-M Law does a great job of summarizing actual insurance data—often even more accurately than traditional assumptions used.

The Z-M Law does better than other distributions at reflecting the risk that a select few accounts will contribute a relatively large number of overall claims. Being able to account for the policies with multiple claims has a wide variety of potential uses in the industry; insurers could be better equipped to identify the biggest risks taken when writing policies, helping to fine-tune pricing and set policy limits and deductible options on coverages.

Particularly when trying to account for the various scenarios where multiple claims combine to exceed the aggregate limit on a single account. Using this new distribution, actuaries can get a better handle on pricing policy limits, particularly when trying to account for various scenarios that would exceed the aggregate limits through multiple claims from a single account. At Verisk, we’re continually researching ways to help refine pricing. Finding unexpected new applications for decades-old distributions is just one example of how our actuarial team works hard to innovate in this space.

Helping to advance actuarial science—by creating a range of effective products that can help streamline workflows—is part of what we do.

Read the study here.

Ralph Dweck

Ralph Dweck is senior actuarial consultant for ISO commercial lines at Verisk. You can contact him at

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