
Mahler alternative method of estimating R(L)
 use direct calculation at low limits
 use a fitted curve at higher limits
 mean residual life (MRL): $ expected XS of L given claim > L

Steps to combine R(L) data
 truncate at d
 Fy(x) = 0 if x ≤ d
 Fy(x) = F_{x}(x)  F_{x}(d) / (1  F_{x}(d)) otherwise
 shift to zero: F_{w}(x) = F_{y}(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)^{s}
 Exponential: cdf = 1  e^{x/c}; R(r) = e^{r}
 F(x;s,b,c) = pA(x) + (1p)B(x)
 R_{F}(L) = [pm_{A}R_{A}(L) + (1p)m_{B}R_{B}(L)\ / [pm_{A}  (1p)m_{B}]
 (+) R(L) closer fit (influenced by 4 parameters)
 (+) for midlvl values, steady drop off similar to exponential, and pareto keeps R(L) from deteriorating too quickly at high values
 R(L), L>d = (base using data) * R(hat)(L  d)

Truncation point
 low enough to have enough data to fit reasonable curve
 high enough that it provides a reasonable ballast to the base factor

