15.4.3 LOGNORMAL MODEL FOR SEVERITIES
In general, one can use the methodology summarized by Equation (15.68) to develop a model combining external data, internal data, and expert opinion for estimation of the severity. For illustration purposes, this section considers the LogNormal severity model; the Pareto severity model is developed in the next section.
Consider modeling severities X1, …, XK ,… using LogNormal (μ, σ 2), where X = (X1,…, XK) are the losses over past T years. Here, we take an approach considered in Section 15.2.4, where μ is unknown and σ is known. The unknown μ is treated under the Bayesian approach as a random variable Θμ. Then combining external data, internal data, and expert opinions can be accomplished using the following model.