because these are evaluated pointwise. The timing for Monte Carlo would be unchanged. The timing for Panjer would be roughly the proportion s$_{0}$/ $40 m of the total timing, because it is evaluated sequentially, from small to large values of s . We continue to consider one-year losses, but now treat the losses from each event as random, not fixed. For the simplest possible generalisation we use a Gamma distribution with a specified expectation x$_{i}$ and a common specified coefficient of variation, θ := σ$_{i}$/x$_{i}$ . The previous case of a fixed loss x$_{i}$ is represented by lim θ → 0, which we write, informally, as θ = 0. Solving gives the two Gamma distribution parameters as Figure 4 shows the effect of varying θ on a Gamma distribution with expec- tation $1 m. The only practical difficulty with allowing random losses for each event occurs for the Panjer method; we describe our approach in the Appendix. Figure 5 shows the exceedance probability curve with θ = 0 . 5: note that the horizontal scale now covers a much wider range of loss values than Figure 3. The timings are given in Table V: these are very similar to the 6.3 Gamma thickening of the event losses x$_{i}$ = α$_{i}$ β$_{i}$ and θx$_{i}$ = √ α$_{i}$ β 2 i α$_{i}$ = 1 θ 2 and β$_{i}$ = α$_{i}$ x$_{i}$ . 22