a = 0.66 , b=1. e = Estimated .02 quantile, s = Simulated .02 quantile, from 1,000,000 simulations (each summing n Paretos). n: e: s: -------------------------------------- 1 1.041255 1.031055 1.009893 2 2.391653 2.363835 1.011768 3 4.10726 4.073608 1.008261 4 6.158219 6.133422 1.004043 5 8.518121 8.488799 1.003454 6 11.16581 11.17158 0.9994833 7 14.08406 14.07764 1.000456 8 17.25850 17.24797 1.000610 9 20.67693 20.70107 0.9988338 10 24.32879 24.38987 0.9974958 11 28.20487 28.34363 0.9951042 12 32.29696 32.3957 0.9969521 13 36.59777 36.75399 0.9957497 14 41.10071 41.25005 0.9963796 15 45.79978 46.00224 0.995599 16 50.68954 50.99908 0.9939305 17 55.76495 56.0973 0.9940755 18 61.02141 61.41345 0.9936163 19 66.45462 66.90487 0.9932702 20 72.06059 72.55279 0.993216 21 77.83561 78.1469 0.9960167 22 83.7762 84.4607 0.9918956 23 89.87908 90.45668 0.9936145 24 96.14118 96.6066 0.9951823 25 102.5596 103.1936 0.9938558 26 109.1316 109.8224 0.99371 27 115.8545 116.6082 0.9935366 28 122.7260 123.3809 0.9946918 29 129.7436 130.8778 0.9913339 30 136.9051 138.1531 0.9909662 31 144.2084 145.3155 0.9923811 32 151.6514 152.7535 0.992785 33 159.2322 160.2709 0.9935188 34 166.9489 168.4274 0.9912218 35 174.7997 176.2457 0.9917956 36 182.7829 184.4470 0.9909779 37 190.8969 192.7732 0.9902668 38 199.1400 200.8589 0.991442 39 207.5106 208.9079 0.9933117 40 216.0075 217.3292 0.993918 41 224.6290 225.5919 0.9957314 42 233.3738 235.0602 0.9928256 43 242.2405 244.308 0.9915375 44 251.228 253.2122 0.992164 45 260.3349 262.8244 0.9905277 46 269.56 271.7386 0.9919828 47 278.9022 280.662 0.9937297 48 288.3603 290.5091 0.9926033 49 297.9331 300.219 0.992386 50 307.6197 309.9542 0.9924683 51 317.419 319.9872 0.9919741 52 327.33 329.6692 0.9929044 53 337.3516 340.1075 0.991897 54 347.483 349.9032 0.993083 55 357.7231 360.3624 0.992676 56 368.0712 370.9359 0.9922769 57 378.5262 381.9197 0.9911146 58 389.0873 392.6075 0.9910338 59 399.7537 403.6549 0.9903353 60 410.5246 414.5235 0.990353 61 421.3991 424.4041 0.9929194 62 432.3764 436.3133 0.9909768 63 443.4559 447.5412 0.9908715 64 454.6367 458.2826 0.9920444 65 465.9180 469.9147 0.991495 66 477.2993 480.617 0.993097 67 488.7798 493.3681 0.9907 68 500.3588 505.3233 0.9901755 69 512.0355 515.5704 0.9931439 70 523.8095 527.952 0.9921537 71 535.6799 539.785 0.992395 72 547.6463 551.3965 0.9931988 73 559.7079 563.2634 0.9936878 74 571.8642 576.4441 0.9920548 75 584.1145 587.356 0.9944811 76 596.4583 601.7448 0.9912147 77 608.895 614.5236 0.9908408 78 621.424 626.061 0.9925935 79 634.0449 640.213 0.9903655 80 646.757 652.1266 0.991766 81 659.5597 665.2369 0.991466 82 672.4527 677.7058 0.9922487 83 685.4353 691.6122 0.9910688 84 698.5071 705.155 0.9905724 85 711.6676 715.892 0.994099 86 724.9162 730.7322 0.9920408 87 738.2525 745.416 0.99039 88 751.6761 757.6116 0.9921655 89 765.1864 771.4088 0.9919338 90 778.783 785.4736 0.9914821 91 792.4655 800.1445 0.990403 92 806.2334 813.5275 0.991034 93 820.0863 826.7715 0.991914 94 834.0237 841.4395 0.9911868 95 848.0452 856.1535 0.9905295 96 862.1505 870.2286 0.9907173 97 876.339 886.0215 0.989072 98 890.6105 899.2412 0.9904022 99 904.9644 913.4673 0.9906916 100 919.4004 927.916 0.990823 1000 33088.77 33364.88 0.9917243 2000 95988.38 96879.43 0.9908025