Modeling Insurance Frequency with the Zipf-Mandelbrot Distribution

To model property/casualty insurance frequency for various lines of business, the Negative Binomial (NB) has long been the distribution of choice, despite evidence that this model often does not fit empirical data sufficiently well. Seeking a different distribution that tends to provide a better fit and is yet simple to use, we investigated the use of the Zipf Mandelbrot (ZM) distribution for fitting insurance frequency. We found, for the various lines of business and sub-groupings of data used in this research (based on increased limit factor tables published by Insurance Services Office), that the Zipf-Mandelbrot distribution regularly gave a better (often drastically better) fit to the data. The relativity-based nature of the Zipf-Mandelbrot (a Pareto-based power-law) is discussed, and several potential pros and cons of using this seemingly unknown distribution are commented on.