a = 0.66 , b=1. e = Estimated .02 quantile, s = Simulated .02 quantile, from 100,000 simulations, (each summing n Paretos), r = e/s. n: e: s: r: -------------------------------------- 1 1.041255 1.030559 1.010379 2 2.391653 2.367816 1.010067 3 4.10726 4.076348 1.007583 4 6.158219 6.134062 1.003938 5 8.518121 8.514283 1.000451 6 11.16581 11.18641 0.9981588 7 14.08406 14.10740 0.9983452 8 17.25850 17.09185 1.00975 9 20.67693 20.63155 1.002199 10 24.32879 24.38113 0.9978534 11 28.20487 28.16081 1.001564 12 32.29696 32.2505 1.001441 13 36.59777 36.76442 0.9954671 14 41.10071 41.13108 0.9992616 15 45.79978 46.41267 0.9867947 16 50.68954 51.09066 0.9921487 17 55.76495 55.76176 1.000057 18 61.02141 60.84199 1.002949 19 66.45462 66.28465 1.002564 20 72.06059 72.32759 0.9963085 21 77.83561 77.92359 0.998871 22 83.7762 83.74721 1.000346 23 89.87908 91.22032 0.9852967 24 96.14118 96.51877 0.996088 25 102.5596 103.0493 0.9952479 26 109.1316 109.3145 0.998327 27 115.8545 116.8187 0.9917461 28 122.7260 123.4911 0.9938045 29 129.7436 130.9012 0.9911568 30 136.9051 138.0607 0.9916296 31 144.2084 145.7 0.9897623 32 151.6514 153.6803 0.9867982 33 159.2322 161.3277 0.9870106 34 166.9489 168.8593 0.9886865 35 174.7997 175.8555 0.9939966 36 182.7829 183.8077 0.9944248 37 190.8969 191.8065 0.9952578 38 199.1400 201.6478 0.9875633 39 207.5106 207.9928 0.997682 40 216.0075 219.4088 0.9844977 41 224.6290 226.2712 0.9927422 42 233.3738 235.8780 0.9893835 43 242.2405 245.5886 0.9863674 44 251.228 253.8427 0.9896994 45 260.3349 263.3895 0.9884026 46 269.56 272.4977 0.9892193 47 278.9022 280.6882 0.993637 48 288.3603 290.5194 0.992568 49 297.9331 300.8784 0.990211 50 307.6197 308.4098 0.9974382 51 317.419 320.4799 0.990449 52 327.33 330.8149 0.9894658 53 337.3516 340.531 0.9906634 54 347.483 349.381 0.9945675 55 357.7231 360.8778 0.9912584 56 368.0712 373.0071 0.9867671 57 378.5262 379.7072 0.9968896 58 389.0873 390.1397 0.9973025 59 399.7537 401.8108 0.9948804 60 410.5246 413.7404 0.9922275 61 421.3991 426.5788 0.9878575 62 432.3764 436.2578 0.991103 63 443.4559 451.2919 0.9826364 64 454.6367 456.1866 0.9966023 65 465.9180 469.6401 0.9920748 66 477.2993 480.8285 0.9926602 67 488.7798 487.5921 1.002436 68 500.3588 500.6202 0.9994778 69 512.0355 518.3118 0.987891 70 523.8095 525.5198 0.9967455 71 535.6799 538.5472 0.994676 72 547.6463 551.6888 0.9926725 73 559.7079 560.2477 0.9990364 74 571.8642 575.8785 0.9930292 75 584.1145 588.0013 0.9933897 76 596.4583 601.3068 0.9919367 77 608.895 614.942 0.9901665 78 621.424 627.175 0.9908304 79 634.0449 638.19 0.9935049 80 646.757 650.3399 0.9944907 81 659.5597 668.3483 0.9868503 82 672.4527 681.772 0.9863306 83 685.4353 687.6289 0.9968099 84 698.5071 701.1807 0.996187 85 711.6676 718.3116 0.9907505 86 724.9162 732.4743 0.9896814 87 738.2525 748.3695 0.9864813 88 751.6761 756.6433 0.9934352 89 765.1864 769.2509 0.9947163 90 778.783 789.9688 0.9858402 91 792.4655 797.6687 0.993477 92 806.2334 809.831 0.9955576 93 820.0863 826.5678 0.9921585 94 834.0237 839.7231 0.9932128 95 848.0452 852.5575 0.9947073 96 862.1505 867.5199 0.9938106 97 876.339 879.6332 0.996255 98 890.6105 894.0551 0.9961471 99 904.9644 921.2529 0.9823192 100 919.4004 920.1914 0.9991404