Loss Models: From Data to Decisions, 4th Edition

19.3 Semi parametric estimation

In some situations it may be reasonable to assume a parametric form for the conditional distribution . The situation at hand may suggest that such an assumption is reasonable or prior information may imply its appropriateness.

For example, in dealing with numbers of claims, it may be reasonable to assume that the number of claims m_ij X_ij for policyholder i in year j is Poisson distributed with mean m_ijθ_i given _i = θ_i. Thus E(m_ijX_ij|_i) = Var(m_ijX_ij|_i) = m_iji, implying that μ(_i) = v(_i) = _i, and so μ = v in this case. Rather than use (19.13) to estimate v, we could use to estimate v.

EXAMPLE 19.6

In the past year, the distribution of automobile insurance policyholders ...