New Feature Request: Pareto

[Andy-Feng-FCAS]

LSM's current parameterization of Pareto is not the more commonly used form of Pareto used in the actuarial community. For example, ISO's parameterization of Pareto could not be directly used in LSM, and must be converted.

It would be better if we could either modify the definition of pareto to Pareto Lomax or add a new distribution in the fitting and simulation process.

[joemarker2]

The "Pareto" distribution in the LSM (Loss Simulation Model) is not the same Pareto distribution that Property-Casualty actuarial science most commonly uses. This has caused confusion among model users.

The "Pareto" distribution that the LSM recognizes is commonly known as the "Pareto Type I" distribution. The Pareto Type I is also known as the Single Parameter Pareto in KPW, the Pareto in Wikipedia, and the "pareto1" in the R "actuar" package. KPW refers to Loss Models, from Data to Decisions, Fourth Edition (2012), by Stuart Klugman, Harry Panjer, and Gordon Willmot. In my experience, applying the fitdistr procedure to fit data to the Pareto Type I distribution does not always converge (see detailed note below).

The "Pareto" distribution commonly used by P&C actuaries has two parameters, shape and scale, with distribution function F(x) = 1 – [ (theta / (theta +x) ) ^ alpha]. This distribution is the "Pareto Type II Lomax" in the KPW book and is the "pareto" in the R "actuar" package. The LSM currently does not support this distribution.

Handling the Pareto Type II distribution would be a good enhancement for the LSM. I would not delete the Pareto Type 1 from the model. My understanding is that Pareto Type I is used in reinsurance work.

Detailed note on non-convergence of fitting the Pareto Type I distribution:
To get convergence, try the "fitdist" procedure from the R package "fitdistrplus". If this still fails, use fitdist but set parameters: method="mge", gof = "CvM"