POT-Based Estimation of the Renewal Function of Interoccurrence Times of Heavy-Tailed Risks

Figure 1

Plots of the new and sample estimators of the renewal function, of interoccurrence times of Pareto-distributed claims with tail indices 2/3 (a) and 3/4 (b), versus the sample size. The horizontal line represents the true value of the renewal function $ℝ(t)$ evaluated at $t=4.$

(a)

(b)