# B.04.Mahler 3

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Mahler alternative method of estimating R(L) use direct calculation at low limitsuse a fitted curve at higher limitsmean residual life (MRL): \$ expected XS of L given claim > L Steps to combine R(L) data truncate at dFy(x) = 0 if x ≤ dFy(x) = Fx(x) - Fx(d) / (1 - Fx(d)) otherwiseshift to zero: Fw(x) = Fy(x+d)normalize to achieve mean unity Mahler's mixture mixture of Pareto A(x;s,b) & exponential B(x;c)Pareto: cdf = 1 - (1 + x/b)-sExponential: cdf = 1 - e-x/c; R(r) = e-rF(x;s,b,c) = pA(x) + (1-p)B(x)RF(L) = [pmARA(L) + (1-p)mBRB(L)\ / [pmA - (1-p)mB](+) R(L) closer fit (influenced by 4 parameters)(+) for mid-lvl values, steady drop off similar to exponential, and pareto keeps R(L) from deteriorating too quickly at high valuesR(L), L>d = (base using data) * R(hat)(L - d) Truncation point low enough to have enough data to fit reasonable curvehigh enough that it provides a reasonable ballast to the base factor AuthorExam8 ID166005 Card SetB.04.Mahler 3 DescriptionWorkers Compensation Excess Ratios: An Alternative Method of Estimation Updated2012-08-14T18:07:35Z Show Answers