The Pareto Distribution and Method of Moments

On why it doesn’t really make sense to fit a Pareto distribution with a method of moments.

I was sent some large loss modelling recently by another actuary for a UK motor book. In the modelling, they had taken the historic large losses, and fit a Pareto distribution using a method of moments. I thought about it for a while and realized that it didn't really like the approach for a couple of reasons which I'll go into in more detail below, but then when I thought about it some more I realised I'd actually seen the exact approach before ... in an IFoA exam paper. So even though the method has some shortcomings, it is actually a taught technique. [1] 

Following the theme from last time, of London's old vs new side by side. Here's a cool photo which shows the old royal naval college in Greenwich, with Canary Wharf in the background. Photo by Fas Khan

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