PENNSYLVANIA COMPENSATION RATING BUREAU. Empirical Pennsylvania Loss Distribution
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1 Exhibit 22 As Filed Corrected-12/17/2015 PENNSYLVANIA COMPENSATION RATING BUREAU Empirical Pennsylvania Loss Distribution Pages 1 through 4 of the attached exhibit present a distribution of Pennsylvania losses by size of claim. The losses used to produce this distribution include three years of experience. Losses have been trended to the midpoint of the experience period for the proposed loss costs and adjusted to reflect current benefit levels. Additionally, losses were brought to an ultimate level by applying development factors to open claims. Page 5 of the exhibit shows a summary and includes loss ranges consistent with those published with the excess loss factors. In certain instances it was necessary to interpolate between loss size ranges in the empirical distribution in deriving excess loss factors for specified limits. The PCRB s analysis this year again considered loss distributions by type of injury based solely on Pennsylvania experience. Pages 6 through 9 of this exhibit show excess loss ratios by loss limitation separately for death, permanent total, permanent partial, temporary total and medicalonly claims. The columns labeled Actual represent excess losses based entirely on actual losses. For each type of injury except medical-only, losses of $500,000 and higher were fitted to a loss distribution curve and actual losses and claim counts were replaced by the fitted values. Cumulative losses and claim counts were then recalculated using fitted values above $500,000 and actual values for loss limitations below $500,000. The resulting excess loss ratios are shown in the column labeled Fitted. Please Note: The term Pareto refers to Single Parameter Pareto Distribution. Page 10 is a graph showing the cumulative loss distribution for the above mentioned types of injury, along with the total for all injuries. The y-axis represents the cumulative percentage of total incurred losses.
2 LIMITS PENNSYLVANIA ACCUMULATED NUMBER ACCUMULATED INDEMNITY EXCESS CLAIMS OF LOSSES AND RATIO AVERAGE (ADDED UP) CLAIMS (ADDED DOWN) MEDICAL , ,636 $ 129,738,626 $ 129,738, $ 430 1,000 1, ,847 75,046 $ 235,151,794 $ 105,413, $ 1,405 2,000-2, ,801 30,962 $ 311,014,386 $ 75,862, $ 2,450 3,000-3, ,839 18,462 $ 374,976,831 $ 63,962, $ 3,465 4,000-4, ,377 12,453 $ 430,682,621 $ 55,705, $ 4,473 5,000-5, ,924 9,590 $ 483,267,802 $ 52,585, $ 5,483 6,000-6, ,334 7,759 $ 533,547,658 $ 50,279, $ 6,480 7,000-7,999 92,575 6,181 $ 579,827,078 $ 46,279, $ 7,487 8,000-8,999 86,394 5,468 $ 626,249,259 $ 46,422, $ 8,490 9,000-9,999 80,926 4,528 $ 669,180,702 $ 42,931, $ 9,481 10,000-10,999 76,398 3,884 $ 709,898,343 $ 40,717, $ 10,483 11,000-11,999 72,514 3,560 $ 750,783,475 $ 40,885, $ 11,485 12,000-12,999 68,954 3,108 $ 789,600,483 $ 38,817, $ 12,489 13,000-13,999 65,846 2,857 $ 828,147,612 $ 38,547, $ 13,492 14,000-14,999 62,989 2,502 $ 864,398,741 $ 36,251, $ 14,489 15,000-15,999 60,487 2,184 $ 898,234,707 $ 33,835, $ 15,493 16,000-16,999 58,303 2,048 $ 932,024,627 $ 33,789, $ 16,499 17,000-17,999 56,255 1,817 $ 963,811,436 $ 31,786, $ 17,494 18,000-18,999 54,438 1,741 $ 996,010,627 $ 32,199, $ 18,495 19,000-19,999 52,697 1,572 $ 1,026,651,565 $ 30,640, $ 19,492 20,000-20,999 51,125 1,445 $ 1,056,267,843 $ 29,616, $ 20,496 21,000-21,999 49,680 1,394 $ 1,086,226,637 $ 29,958, $ 21,491 22,000-22,999 48,286 1,316 $ 1,115,825,892 $ 29,599, $ 22,492 23,000-23,999 46,970 1,238 $ 1,144,914,352 $ 29,088, $ 23,496 24,000-24,999 45,732 1,112 $ 1,172,148,864 $ 27,234, $ 24,491 25,000-25,999 44,620 1,095 $ 1,200,086,917 $ 27,938, $ 25,514 26,000-26,999 43, $ 1,226,465,091 $ 26,378, $ 26,484 27,000-27,999 42,529 1,004 $ 1,254,081,141 $ 27,616, $ 27,506 28,000-28,999 41, $ 1,279,845,358 $ 25,764, $ 28,500 29,000-29,999 40, $ 1,305,786,960 $ 25,941, $ 29,479 30,000-30,999 39, $ 1,331,610,454 $ 25,823, $ 30,488 31,000-31,999 38, $ 1,356,463,949 $ 24,853, $ 31,500 32,000-32,999 38, $ 1,380,317,743 $ 23,853, $ 32,498 33,000-33,999 37, $ 1,402,431,385 $ 22,113, $ 33,506 34,000-34,999 36, $ 1,426,923,230 $ 24,491, $ 34,496 35,000-35,999 36, $ 1,450,480,333 $ 23,557, $ 35,478 36,000-36,999 35, $ 1,472,921,867 $ 22,441, $ 36,490 37,000-37,999 34, $ 1,495,460,059 $ 22,538, $ 37,501 38,000-38,999 34, $ 1,518,064,075 $ 22,604, $ 38,508 39,000-39,999 33, $ 1,539,188,154 $ 21,124, $ 39,484 40,000-40,999 32, $ 1,560,609,031 $ 21,420, $ 40,493 41,000-41,999 32, $ 1,582,596,383 $ 21,987, $ 41,486 42,000-42,999 31, $ 1,603,205,223 $ 20,608, $ 42,492 43,000-43,999 31, $ 1,623,259,689 $ 20,054, $ 43,502 44,000-44,999 30, $ 1,644,533,704 $ 21,274, $ 44,506 45,000-45,999 30, $ 1,667,555,232 $ 23,021, $ 45,497 46,000-46,999 30, $ 1,686,342,042 $ 18,786, $ 46,502 47,000-47,999 29, $ 1,706,001,966 $ 19,659, $ 47,488 48,000-48,999 29, $ 1,726,117,181 $ 20,115, $ 48,470 49,000-49,999 28, $ 1,744,629,831 $ 18,512, $ 49,499 1
3 ACCUMULATED NUMBER ACCUMULATED INDEMNITY EXCESS LIMITS CLAIMS OF LOSSES AND RATIO AVERAGE (ADDED UP) CLAIMS (ADDED DOWN) MEDICAL 50,000-50,999 28, $ 1,763,212,261 $ 18,582, $ 50,496 51,000-51,999 28, $ 1,782,061,125 $ 18,848, $ 51,500 52,000-52,999 27, $ 1,801,212,148 $ 19,151, $ 52,469 53,000-53,999 27, $ 1,820,256,844 $ 19,044, $ 53,496 54,000-54,999 26, $ 1,837,311,545 $ 17,054, $ 54,488 55,000-55,999 26, $ 1,855,958,508 $ 18,646, $ 55,497 56,000-56,999 26, $ 1,874,101,342 $ 18,142, $ 56,520 57,000-57,999 25, $ 1,892,966,218 $ 18,864, $ 57,515 58,000-58,999 25, $ 1,912,390,044 $ 19,423, $ 58,506 59,000-59,999 25, $ 1,929,877,249 $ 17,487, $ 59,480 60,000-60,999 25, $ 1,945,127,568 $ 15,250, $ 60,517 61,000-61,999 24, $ 1,959,706,112 $ 14,578, $ 61,513 62,000-62,999 24, $ 1,976,523,077 $ 16,816, $ 62,517 63,000-63,999 24, $ 1,991,951,951 $ 15,428, $ 63,493 64,000-64,999 24, $ 2,007,753,223 $ 15,801, $ 64,495 65,000-65,999 23, $ 2,023,476,872 $ 15,723, $ 65,515 66,000-66,999 23, $ 2,039,831,228 $ 16,354, $ 66,481 67,000-67,999 23, $ 2,054,137,443 $ 14,306, $ 67,482 68,000-68,999 23, $ 2,066,950,537 $ 12,813, $ 68,519 69,000-69,999 22, $ 2,081,478,500 $ 14,527, $ 69,512 70,000-70,999 22, $ 2,096,557,347 $ 15,078, $ 70,462 71,000-71,999 22, $ 2,111,215,236 $ 14,657, $ 71,502 72,000-72,999 22, $ 2,125,212,173 $ 13,996, $ 72,523 73,000-73,999 22, $ 2,140,134,081 $ 14,921, $ 73,507 74,000-74,999 21, $ 2,156,151,540 $ 16,017, $ 74,500 75,000-75,999 21, $ 2,172,149,902 $ 15,998, $ 75,464 76,000-76,999 21, $ 2,188,373,799 $ 16,223, $ 76,528 77,000-77,999 21, $ 2,204,422,076 $ 16,048, $ 77,528 78,000-78,999 21, $ 2,219,738,288 $ 15,316, $ 78,545 79,000-79,999 20, $ 2,233,489,278 $ 13,750, $ 79,485 80,000-80,999 20, $ 2,248,787,472 $ 15,298, $ 80,517 81,000-81,999 20, $ 2,264,036,840 $ 15,249, $ 81,547 82,000-82,999 20, $ 2,276,818,242 $ 12,781, $ 82,461 83,000-83,999 20, $ 2,291,095,295 $ 14,277, $ 83,492 84,000-84,999 19, $ 2,303,521,515 $ 12,426, $ 84,532 85,000-85,999 19, $ 2,316,004,462 $ 12,482, $ 85,500 86,000-86,999 19, $ 2,329,752,175 $ 13,747, $ 86,464 87,000-87,999 19, $ 2,342,697,558 $ 12,945, $ 87,469 88,000-88,999 19, $ 2,356,413,789 $ 13,716, $ 88,492 89,000-89,999 19, $ 2,369,836,697 $ 13,422, $ 89,486 90,000-90,999 19, $ 2,385,133,495 $ 15,296, $ 90,514 91,000-91,999 18, $ 2,397,674,328 $ 12,540, $ 91,539 92,000-92,999 18, $ 2,412,747,988 $ 15,073, $ 92,476 93,000-93,999 18, $ 2,425,932,371 $ 13,184, $ 93,506 94,000-94,999 18, $ 2,438,019,979 $ 12,087, $ 94,434 95,000-95,999 18, $ 2,454,542,721 $ 16,522, $ 95,507 96,000-96,999 18, $ 2,467,569,005 $ 13,026, $ 96,491 97,000-97,999 18, $ 2,481,418,087 $ 13,849, $ 97,529 98,000-98,999 17, $ 2,494,522,820 $ 13,104, $ 98,532 99,000-99,999 17, $ 2,506,964,384 $ 12,441, $ 99, , ,999 17,601 1,277 $ 2,640,903,560 $ 133,939, $ 104,886 2
4 ACCUMULATED NUMBER ACCUMULATED INDEMNITY EXCESS LIMITS CLAIMS OF LOSSES AND RATIO AVERAGE (ADDED UP) CLAIMS (ADDED DOWN) MEDICAL 110, ,999 16,324 1,184 $ 2,776,997,611 $ 136,094, $ 114, , ,999 15,140 1,062 $ 2,909,537,682 $ 132,540, $ 124, , ,999 14, $ 3,040,157,369 $ 130,619, $ 134, , ,999 13, $ 3,180,202,548 $ 140,045, $ 144, , ,999 12, $ 3,311,104,516 $ 130,901, $ 154, , ,999 11, $ 3,438,711,160 $ 127,606, $ 164, , ,999 10, $ 3,560,774,056 $ 122,062, $ 174, , ,999 9, $ 3,679,277,192 $ 118,503, $ 185, , ,999 9, $ 3,799,854,820 $ 120,577, $ 194, , ,999 8, $ 3,908,299,452 $ 108,444, $ 204, , ,999 8, $ 4,014,095,859 $ 105,796, $ 215, , ,999 7, $ 4,119,396,520 $ 105,300, $ 225, , ,999 7, $ 4,221,291,880 $ 101,895, $ 234, , ,999 6, $ 4,314,693,824 $ 93,401, $ 245, , ,999 6, $ 4,403,032,821 $ 88,338, $ 255, , ,999 5, $ 4,481,702,812 $ 78,669, $ 264, , ,999 5, $ 4,569,680,062 $ 87,977, $ 274, , ,999 5, $ 4,650,227,800 $ 80,547, $ 284, , ,999 5, $ 4,735,482,459 $ 85,254, $ 294, , ,999 4, $ 4,841,528,355 $ 106,045, $ 307, , ,999 4, $ 4,938,945,712 $ 97,417, $ 322, , ,999 4, $ 5,032,343,301 $ 93,397, $ 337, , ,999 3, $ 5,126,820,141 $ 94,476, $ 352, , ,999 3, $ 5,206,519,501 $ 79,699, $ 367, , ,999 3, $ 5,289,109,186 $ 82,589, $ 382, , ,999 3, $ 5,356,363,465 $ 67,254, $ 397, , ,999 2, $ 5,412,829,126 $ 56,465, $ 412, , ,999 2, $ 5,494,267,543 $ 81,438, $ 430, , ,999 2, $ 5,581,245,589 $ 86,978, $ 450, , ,999 2, $ 5,652,205,690 $ 70,960, $ 469, , ,999 2, $ 5,725,695,329 $ 73,489, $ 489, , ,999 2, $ 5,795,576,339 $ 69,881, $ 510, , ,999 1, $ 5,854,785,145 $ 59,208, $ 528, , ,999 1, $ 5,905,998,282 $ 51,213, $ 550, , ,999 1, $ 5,951,064,710 $ 45,066, $ 570, , ,999 1, $ 6,008,905,683 $ 57,840, $ 590, , ,999 1, $ 6,077,039,339 $ 68,133, $ 613, , ,999 1, $ 6,151,243,114 $ 74,203, $ 645, , ,999 1, $ 6,240,814,175 $ 89,571, $ 678, , ,999 1, $ 6,348,223,909 $ 107,409, $ 725, , ,999 1, $ 6,447,406,407 $ 99,182, $ 774, , , $ 6,530,488,789 $ 83,082, $ 822, , , $ 6,619,568,487 $ 89,079, $ 873, , , $ 6,739,433,046 $ 119,864, $ 951,306 1,000,000-1,099, $ 6,855,688,712 $ 116,255, $ 1,047,348 1,100,000-1,199, $ 6,935,678,839 $ 79,990, $ 1,142,716 1,200,000-1,299, $ 7,005,365,645 $ 69,686, $ 1,244,407 1,300,000-1,399, $ 7,086,331,690 $ 80,966, $ 1,349,434 1,400,000-1,499, $ 7,153,080,519 $ 66,748, $ 1,451,062 1,500,000-1,599, $ 7,193,496,207 $ 40,415, $ 1,554,450 1,600,000-1,699, $ 7,242,908,139 $ 49,411, $ 1,647,064 3
5 ACCUMULATED NUMBER ACCUMULATED INDEMNITY EXCESS LIMITS CLAIMS OF LOSSES AND RATIO AVERAGE (ADDED UP) CLAIMS (ADDED DOWN) MEDICAL 1,700,000-1,799, $ 7,288,176,916 $ 45,268, $ 1,741,107 1,800,000-1,899, $ 7,327,132,794 $ 38,955, $ 1,855,042 1,900,000-1,999, $ 7,358,281,336 $ 31,148, $ 1,946,784 2,000,000-2,999, $ 7,597,362,549 $ 239,081, $ 2,439,604 3,000,000-3,999, $ 7,691,116,516 $ 93,753, $ 3,472,369 4,000,000-4,999, $ 7,753,588,675 $ 62,472, $ 4,462,297 5,000,000-5,999, $ 7,775,116,911 $ 21,528, $ 5,382,059 6,000,000-6,999, $ 7,826,986,041 $ 51,869, $ 6,483,641 7,000,000-7,999, $ 7,872,302,244 $ 45,316, $ 7,552,701 8,000,000-8,999, $ 7,896,895,829 $ 24,593, $ 8,197,862 9,000,000-9,999, $ 7,906,561,104 $ 9,665, $ 9,665,275 10,000,000 - AND GREATER $ 8,035,792,924 $ 129,231, $ 12,923,182 GRAND TOTALS 548,483 EXCLUDING CONTRACT MEDICAL $ 8,035,792,924 $ 14,651 4
6 Pennsylvania Compensation Rating Bureau Distribution of Losses Excess Loss Limits * Loss Number Excess Loss Average Empirical From TO (<) Amount of Claims Amount Excess Ratio 8,035,792, , ,180, ,085 6,602,632,222 1, ,000 15, ,218,039 15,911 6,264,089,183 12, ,000 20, ,252,824 9,362 5,986,641,359 17, ,000 25, ,497,299 6,505 5,748,144,060 22, ,000 30, ,638,096 4,879 5,537,775,964 27, ,000 35, ,136,270 3,740 5,348,834,694 32, ,000 40, ,264,924 3,002 5,176,644,770 37, ,000 50, ,441,677 4,596 4,871,013,093 44, ,000 75, ,521,709 6,749 4,255,591,384 60, , , ,812,844 4,053 3,768,728,540 86, , , ,303,263 2,992 3,366,400, , , , ,934,902 2,465 3,033,990, , , , ,540,060 1,968 2,755,250, , , , ,112,212 1,608 2,522,338, , , , ,891,370 1,255 2,323,621, , , , ,947,635 1,049 2,155,099, , , , ,997, ,008,326, , , , ,791, ,881,610, , , , ,990, ,769,952, , , , ,362, ,671,474, , , , ,683, ,584,273, , , , ,425, ,505,314, , , ,000 99,243, ,433,535, , , , ,567, ,367,411, , , ,000 96,709, ,307,521, , , ,000 91,229, ,252,597, , , , ,210, ,069,287, , , , ,908, ,378, , , , ,592, ,786, , , , ,162, ,124, , ,000 1,000, ,864, ,359, , ,000,000 2,000, ,848, ,511,588 1,339, ,000,000 3,000, ,081, ,430,375 2,439, ,000,000 4,000,000 93,753, ,676,408 3,472, ,000,000 5,000,000 62,472, ,204,249 4,462, ,000,000 6,000,000 21,528, ,676,013 5,382, ,000,000 7,000,000 51,869, ,806,883 6,483, ,000,000 8,000,000 45,316, ,490,680 7,552, ,000,000 9,000,000 24,593, ,897,095 8,197, ,000,000 10,000,000 9,665, ,231,820 9,665, ,000,000 & Over 129,231, ,923,182 TOTAL/AVERAGE 8,035,792, ,483 14,651 * Limits consistent with published loss limits for excess loss factors Values have been interpolated when not available on prior pages 5
7 Death-Pareto PT-Lognormal PP-Pareto TT-Pareto Med only Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Loss Excess Excess Excess Excess Excess Excess Excess Excess Excess Limit Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio 1, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
8 Death-Pareto PT-Lognormal PP-Pareto TT-Pareto Med only Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Loss Excess Excess Excess Excess Excess Excess Excess Excess Excess Limit Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio 50, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
9 Death-Pareto PT-Lognormal PP-Pareto TT-Pareto Med only Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Loss Excess Excess Excess Excess Excess Excess Excess Excess Excess Limit Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio 110, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,000, ,100, ,200, ,300, ,400, ,500, ,600,
10 Death-Pareto PT-Lognormal PP-Pareto TT-Pareto Med only Actual Fitted Actual Fitted Actual Fitted Actual Fitted Actual Loss Excess Excess Excess Excess Excess Excess Excess Excess Excess Limit Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio 1,700, ,800, ,900, ,000, ,000, ,000, ,000, ,000, ,000, ,000, ,000, ,000,
11 Pennsylvania Compensation Rating Bureau Cumulative Distribution of Loss By Type of Injury ( ) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Death PT PP TT All 10
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