Here c = the empirical 0.98 quantile for the sum of n Paretos: And we're doing 10 million simulations of each sum. Really 10 million; i.e. when n=5, we're actually generating 50 million Paretos altogether, 5 for each sum. n = 2 a = 0.5 c = 10000.17 n = 2 a = 0.6666667 c = 1012.340 n = 2 a = 1 c = 104.7153 n = 2 a = 1.5 c = 24.01130 n = 5 a = 0.5 c = 62436.65 n = 5 a = 0.6666667 c = 4029.958 n = 5 a = 1 c = 271.3259 n = 5 a = 1.5 c = 50.38605 n = 10 a = 0.5 c = 249338.2 n = 10 a = 0.6666667 c = 11406.04 n = 10 a = 1 c = 555.4726 n = 10 a = 1.5 c = 88.03292 n = 20 a = 0.5 c = 1004949 n = 20 a = 0.6666667 c = 32489.57 n = 20 a = 1 c = 1127.164 n = 20 a = 1.5 c = 153.8022 n = 50 a = 0.5 c = 6237558 n = 50 a = 0.6666667 c = 128040.7 n = 50 a = 1 c = 2888.229 n = 50 a = 1.5 c = 326.4243 n = 100 a = 0.5 c = 25040967 n = 100 a = 0.6666667 c = 363796.4 n = 100 a = 1 c = 5851.764 n = 100 a = 1.5 c = 583.2789