a = 0.8 , b=1. e = Estimated .02 quantile, s = Simulated .02 quantile, from 1,000,000 simulations (each summing n Paretos). n: e: s: -------------------------------------- 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100 1 1.034013 1.025649 1.008154 2 2.316518 2.292067 1.010668 3 3.876763 3.849133 1.007178 4 5.677777 5.656806 1.003707 5 7.690313 7.668991 1.002780 6 9.892211 9.907027 0.9985046 7 12.26617 12.26961 0.9997192 8 14.79826 14.80605 0.9994736 9 17.47699 17.47423 1.000158 10 20.29271 20.3064 0.9993258 11 23.23715 23.26896 0.9986332 12 26.30317 26.34579 0.9983821 13 29.48447 29.58112 0.9967327 14 32.77552 32.85587 0.9975545 15 36.17137 36.24233 0.998042 16 39.66755 39.75654 0.9977615 17 43.26005 43.45098 0.9956059 18 46.9452 47.10961 0.9965102 19 50.71967 50.84878 0.997461 20 54.58036 54.73472 0.99718 21 58.52446 58.69936 0.9970205 22 62.54934 62.75741 0.9966845 23 66.65256 66.83303 0.9972997 24 70.83185 71.15144 0.9955083 25 75.0851 75.3134 0.9969687 26 79.41033 79.70763 0.9962701 27 83.80566 83.95617 0.9982073 28 88.26935 88.44415 0.9980236 29 92.79974 93.16474 0.9960822 30 97.39528 97.70359 0.9968445 31 102.0545 102.4444 0.996194 32 106.7759 107.2915 0.9951945 33 111.5583 112.0150 0.9959236 34 116.4004 117.0344 0.9945832 35 121.3009 121.5860 0.9976555 36 126.2588 126.6535 0.9968833 37 131.2728 131.5948 0.9975536 38 136.3420 136.9123 0.9958345 39 141.4654 141.96 0.996516 40 146.642 147.1121 0.9968048 41 151.8709 152.1542 0.998138 42 157.1511 157.3693 0.9986136 43 162.4819 163.0529 0.996498 44 167.8624 168.4009 0.996802 45 173.2919 173.7233 0.9975166 46 178.7695 179.4179 0.9963857 47 184.2945 184.8643 0.996918 48 189.8663 190.3456 0.997482 49 195.4841 196.1405 0.9966534 50 201.1473 201.8852 0.996345 51 206.8553 207.4312 0.9972236 52 212.6074 213.4642 0.9959864 53 218.4030 219.0489 0.9970514 54 224.2416 225.0663 0.9963358 55 230.1226 230.9904 0.996243 56 236.0455 236.7831 0.996885 57 242.0096 242.6796 0.9972394 58 248.0146 248.8846 0.9965044 59 254.0599 255.2731 0.9952474 60 260.145 260.8048 0.99747 61 266.2694 266.825 0.997918 62 272.4328 273.1175 0.9974932 63 278.6346 280.0492 0.9949487 64 284.8745 285.595 0.9974771 65 291.1519 291.873 0.9975295 66 297.4665 298.1246 0.9977925 67 303.8179 304.4784 0.9978308 68 310.2057 311.1766 0.9968801 69 316.6296 317.6644 0.9967424 70 323.089 323.967 0.9972899 71 329.5837 330.7416 0.9964991 72 336.1134 336.4866 0.9988907 73 342.6776 343.6521 0.9971642 74 349.2761 350.2088 0.9973365 75 355.9084 357.1016 0.9966587 76 362.5744 363.8918 0.9963796 77 369.2736 370.3426 0.9971135 78 376.0057 376.9131 0.9975927 79 382.7705 383.6569 0.9976897 80 389.5677 390.3382 0.998026 81 396.3969 396.8158 0.9989444 82 403.258 404.0161 0.9981236 83 410.1505 410.9337 0.9980941 84 417.0742 418.1276 0.9974807 85 424.0290 425.1597 0.9973405 86 431.0144 432.149 0.9973745 87 438.0302 439.1461 0.997459 88 445.0763 446.1471 0.9975998 89 452.1523 453.8671 0.9962217 90 459.258 460.8473 0.9965514 91 466.3931 468.1916 0.9961587 92 473.5575 475.1198 0.9967118 93 480.7509 482.0135 0.9973806 94 487.9731 489.3518 0.9971827 95 495.2238 496.5116 0.9974064 96 502.5029 503.9866 0.9970562 97 509.8101 511.3509 0.9969868 98 517.1452 518.5309 0.9973276 99 524.5081 526.4789 0.9962567 100 531.8984 532.9396 0.9980464