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Phenomena affecting excess ratios:
 different sizes of claims may have varying expected amounts of development
 dispersion effect: even losses of the same size might develop differently

Simple Dispersion
 R(L) = weighted avg of XS ratios
 E_{i}(X) = expected value of X between x_{i} and x_{i+1}
 R(L) = ∑R_{i}(L)E_{i}(X) / E(X)
 R_{hat}(L)= ∑p_{i}r_{i}R(L/r_{i}) / ∑p_{i}r_{i}
 this allows the severity curve to have different distributions in different parts of the curve
 conclusion: even if losses develop by a factor of 1 on average, the probability of developing higher/lower actually affects R(L) if the severity distribution isn't constant

Generalized Dispersion
 F(y)=∫_{0 to ∞} D(y/r) h(r) dr
 if losses ~ exponential, and loss divisors ~ gamma, developed losses ~ Pareto
 increasing the shape parameter of a Pareto distribution decrease tail and variance
 we can use piecewise linear distribution to estimate distribution in pieces and then weight
 dispersion increases when loss divider has a heavier tail (e.g. gamma)
 dispersion increases when coefficient of variation of the loss divisor distribution increases
 greater dispersion results in greater excess ratios

