PENNSYLVANIA COMPENSATION RATING BUREAU. Empirical Pennsylvania Loss Distribution
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1 Exhibit 22 As Filed 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 Bureau 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 and temporary total claims. The columns labeled Actual represent excess losses based entirely on actual losses. For each type of injury, 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 DISTRIBUTION OF LOSSES(All) ACCUMULATED NUMBER ACCUMULATED INDEMNITY EXCESS CLAIMS OF LOSSES AND RATIO AVERAGE (ADDED UP) CLAIMS (ADDED DOWN) MEDICAL - 1, , ,222 $ 284,504,279 $ 284,504, $ 595 2,000-2, ,860 34,214 $ 368,275,397 $ 83,771, $ 2,448 3,000-3, ,646 20,734 $ 440,119,868 $ 71,844, $ 3,465 4,000-4, ,912 14,106 $ 503,216,540 $ 63,096, $ 4,473 5,000-5, ,806 10,633 $ 561,471,275 $ 58,254, $ 5,479 6,000-6, ,173 8,662 $ 617,614,724 $ 56,143, $ 6,482 7,000-7, ,511 7,330 $ 672,461,221 $ 54,846, $ 7,482 8,000-8,999 96,181 6,107 $ 724,267,276 $ 51,806, $ 8,483 9,000-9,999 90,074 5,334 $ 774,842,095 $ 50,574, $ 9,482 10,000-10,999 84,740 4,749 $ 824,629,078 $ 49,786, $ 10,484 11,000-11,999 79,991 4,120 $ 871,921,716 $ 47,292, $ 11,479 12,000-12,999 75,871 3,568 $ 916,503,232 $ 44,581, $ 12,495 13,000-13,999 72,303 3,198 $ 959,644,532 $ 43,141, $ 13,490 14,000-14,999 69,105 2,907 $ 1,001,756,132 $ 42,111, $ 14,486 15,000-15,999 66,198 2,574 $ 1,041,631,560 $ 39,875, $ 15,492 16,000-16,999 63,624 2,500 $ 1,082,868,269 $ 41,236, $ 16,495 17,000-17,999 61,124 2,122 $ 1,119,972,384 $ 37,104, $ 17,485 18,000-18,999 59,002 2,037 $ 1,157,644,817 $ 37,672, $ 18,494 19,000-19,999 56,965 1,838 $ 1,193,473,099 $ 35,828, $ 19,493 20,000-20,999 55,127 1,641 $ 1,227,088,780 $ 33,615, $ 20,485 21,000-21,999 53,486 1,639 $ 1,262,297,176 $ 35,208, $ 21,482 22,000-22,999 51,847 1,501 $ 1,296,062,541 $ 33,765, $ 22,495 23,000-23,999 50,346 1,385 $ 1,328,602,134 $ 32,539, $ 23,494 24,000-24,999 48,961 1,243 $ 1,359,051,954 $ 30,449, $ 24,497 25,000-25,999 47,718 1,207 $ 1,389,825,405 $ 30,773, $ 25,496 26,000-26,999 46,511 1,140 $ 1,420,035,900 $ 30,210, $ 26,500 27,000-27,999 45,371 1,077 $ 1,449,641,342 $ 29,605, $ 27,489 28,000-28,999 44,294 1,044 $ 1,479,373,430 $ 29,732, $ 28,479 29,000-29,999 43, $ 1,507,425,324 $ 28,051, $ 29,497 30,000-30,999 42, $ 1,535,933,653 $ 28,508, $ 30,490 31,000-31,999 41, $ 1,563,290,051 $ 27,356, $ 31,517 32,000-32,999 40, $ 1,590,543,729 $ 27,253, $ 32,484 33,000-33,999 39, $ 1,615,164,881 $ 24,621, $ 33,498 34,000-34,999 38, $ 1,641,063,249 $ 25,898, $ 34,485 35,000-35,999 38, $ 1,666,973,181 $ 25,909, $ 35,493 36,000-36,999 37, $ 1,692,476,681 $ 25,503, $ 36,486 37,000-37,999 36, $ 1,715,990,885 $ 23,514, $ 37,503 38,000-38,999 36, $ 1,740,324,906 $ 24,334, $ 38,503 39,000-39,999 35, $ 1,763,351,099 $ 23,026, $ 39,496 40,000-40,999 34, $ 1,786,234,822 $ 22,883, $ 40,502 41,000-41,999 34, $ 1,809,147,813 $ 22,912, $ 41,509 42,000-42,999 33, $ 1,833,155,474 $ 24,007, $ 42,491 43,000-43,999 33, $ 1,854,694,514 $ 21,539, $ 43,513 44,000-44,999 32, $ 1,875,432,469 $ 20,737, $ 44,502 45,000-45,999 32, $ 1,895,635,849 $ 20,203, $ 45,503 46,000-46,999 31, $ 1,914,703,513 $ 19,067, $ 46,506 47,000-47,999 31, $ 1,932,612,914 $ 17,909, $ 47,505 48,000-48,999 31, $ 1,951,434,604 $ 18,821, $ 48,510 49,000-49,999 30, $ 1,970,787,617 $ 19,353, $ 49,496 50,000-50,999 30, $ 1,989,271,967 $ 18,484, $ 50,504 1
3 DISTRIBUTION OF LOSSES(All) ACCUMULATED NUMBER ACCUMULATED INDEMNITY EXCESS LIMITS CLAIMS OF LOSSES AND RATIO AVERAGE (ADDED UP) CLAIMS (ADDED DOWN) MEDICAL 51,000-51,999 29, $ 2,007,200,612 $ 17,928, $ 51,519 52,000-52,999 29, $ 2,024,355,357 $ 17,154, $ 52,461 53,000-53,999 29, $ 2,041,478,885 $ 17,123, $ 53,511 54,000-54,999 28, $ 2,059,792,522 $ 18,313, $ 54,505 55,000-55,999 28, $ 2,076,502,623 $ 16,710, $ 55,515 56,000-56,999 28, $ 2,093,795,650 $ 17,293, $ 56,513 57,000-57,999 27, $ 2,109,722,085 $ 15,926, $ 57,496 58,000-58,999 27, $ 2,125,226,376 $ 15,504, $ 58,507 59,000-59,999 27, $ 2,141,109,328 $ 15,882, $ 59,487 60,000-60,999 27, $ 2,156,161,449 $ 15,052, $ 60,450 61,000-61,999 26, $ 2,171,533,655 $ 15,372, $ 61,489 62,000-62,999 26, $ 2,188,222,806 $ 16,689, $ 62,506 63,000-63,999 26, $ 2,203,975,159 $ 15,752, $ 63,518 64,000-64,999 26, $ 2,219,715,100 $ 15,739, $ 64,508 65,000-65,999 25, $ 2,234,774,329 $ 15,059, $ 65,475 66,000-66,999 25, $ 2,248,731,361 $ 13,957, $ 66,462 67,000-67,999 25, $ 2,263,651,418 $ 14,920, $ 67,512 68,000-68,999 25, $ 2,277,832,911 $ 14,181, $ 68,510 69,000-69,999 25, $ 2,292,148,982 $ 14,316, $ 69,495 70,000-70,999 24, $ 2,307,378,927 $ 15,229, $ 70,509 71,000-71,999 24, $ 2,323,962,939 $ 16,584, $ 71,483 72,000-72,999 24, $ 2,339,474,686 $ 15,511, $ 72,485 73,000-73,999 24, $ 2,354,611,871 $ 15,137, $ 73,481 74,000-74,999 23, $ 2,369,439,768 $ 14,827, $ 74,512 75,000-75,999 23, $ 2,382,949,968 $ 13,510, $ 75,476 76,000-76,999 23, $ 2,396,878,682 $ 13,928, $ 76,531 77,000-77,999 23, $ 2,409,361,676 $ 12,482, $ 77,534 78,000-78,999 23, $ 2,422,468,748 $ 13,107, $ 78,485 79,000-79,999 23, $ 2,436,785,655 $ 14,316, $ 79,538 80,000-80,999 22, $ 2,449,257,217 $ 12,471, $ 80,462 81,000-81,999 22, $ 2,463,514,161 $ 14,256, $ 81,468 82,000-82,999 22, $ 2,477,370,819 $ 13,856, $ 82,480 83,000-83,999 22, $ 2,489,394,368 $ 12,023, $ 83,497 84,000-84,999 22, $ 2,502,411,151 $ 13,016, $ 84,525 85,000-85,999 22, $ 2,516,947,640 $ 14,536, $ 85,509 86,000-86,999 21, $ 2,529,751,441 $ 12,803, $ 86,512 87,000-87,999 21, $ 2,541,834,264 $ 12,082, $ 87,557 88,000-88,999 21, $ 2,555,466,701 $ 13,632, $ 88,522 89,000-89,999 21, $ 2,567,278,394 $ 11,811, $ 89,483 90,000-90,999 21, $ 2,581,393,739 $ 14,115, $ 90,483 91,000-91,999 21, $ 2,596,028,826 $ 14,635, $ 91,469 92,000-92,999 21, $ 2,606,855,060 $ 10,826, $ 92,532 93,000-93,999 20, $ 2,618,173,838 $ 11,318, $ 93,544 94,000-94,999 20, $ 2,630,933,105 $ 12,759, $ 94,513 95,000-95,999 20, $ 2,644,108,788 $ 13,175, $ 95,476 96,000-96,999 20, $ 2,655,591,249 $ 11,482, $ 96,491 97,000-97,999 20, $ 2,668,559,559 $ 12,968, $ 97,506 98,000-98,999 20, $ 2,680,278,067 $ 11,718, $ 98,475 99,000-99,999 20, $ 2,692,216,254 $ 11,938, $ 99, , ,999 20,010 1,196 $ 2,817,746,181 $ 125,529, $ 104, , ,999 18,814 1,077 $ 2,941,481,948 $ 123,735, $ 114,889 2
4 DISTRIBUTION OF LOSSES(All) ACCUMULATED NUMBER ACCUMULATED INDEMNITY EXCESS LIMITS CLAIMS OF LOSSES AND RATIO AVERAGE (ADDED UP) CLAIMS (ADDED DOWN) MEDICAL 120, ,999 17, $ 3,060,222,100 $ 118,740, $ 125, , ,999 16, $ 3,177,427,427 $ 117,205, $ 135, , ,999 15, $ 3,305,948,124 $ 128,520, $ 145, , ,999 15, $ 3,446,880,648 $ 140,932, $ 154, , ,999 14, $ 3,583,365,318 $ 136,484, $ 165, , ,999 13, $ 3,712,605,641 $ 129,240, $ 175, , ,999 12, $ 3,840,967,876 $ 128,362, $ 184, , ,999 11, $ 3,967,445,450 $ 126,477, $ 194, , ,999 11, $ 4,080,291,117 $ 112,845, $ 204, , ,999 10, $ 4,207,236,468 $ 126,945, $ 214, , ,999 10, $ 4,322,440,118 $ 115,203, $ 225, , ,999 9, $ 4,432,153,378 $ 109,713, $ 234, , ,999 9, $ 4,533,348,133 $ 101,194, $ 245, , ,999 8, $ 4,634,217,987 $ 100,869, $ 254, , ,999 8, $ 4,735,089,874 $ 100,871, $ 264, , ,999 7, $ 4,836,033,425 $ 100,943, $ 275, , ,999 7, $ 4,932,353,167 $ 96,319, $ 284, , ,999 7, $ 5,029,978,853 $ 97,625, $ 294, , ,999 6, $ 5,162,622,488 $ 132,643, $ 307, , ,999 6, $ 5,296,760,894 $ 134,138, $ 322, , ,999 6, $ 5,418,814,986 $ 122,054, $ 337, , ,999 5, $ 5,538,405,348 $ 119,590, $ 352, , ,999 5, $ 5,642,663,802 $ 104,258, $ 367, , ,999 5, $ 5,759,760,207 $ 117,096, $ 382, , ,999 4, $ 5,864,305,615 $ 104,545, $ 397, , ,999 4, $ 5,966,512,902 $ 102,207, $ 412, , ,999 4, $ 6,093,134,476 $ 126,621, $ 429, , ,999 3, $ 6,224,164,398 $ 131,029, $ 450, , ,999 3, $ 6,355,204,499 $ 131,040, $ 469, , ,999 3, $ 6,454,659,963 $ 99,455, $ 489, , ,999 3, $ 6,560,703,682 $ 106,043, $ 509, , ,999 2, $ 6,670,624,326 $ 109,920, $ 531, , ,999 2, $ 6,767,851,532 $ 97,227, $ 549, , ,999 2, $ 6,857,875,796 $ 90,024, $ 569, , ,999 2, $ 6,949,270,087 $ 91,394, $ 589, , ,999 2, $ 7,061,739,855 $ 112,469, $ 614, , ,999 2, $ 7,178,793,473 $ 117,053, $ 643, , ,999 1, $ 7,306,374,665 $ 127,581, $ 678, , ,999 1, $ 7,464,154,682 $ 157,780, $ 723, , ,999 1, $ 7,616,159,652 $ 152,004, $ 775, , ,999 1, $ 7,748,151,310 $ 131,991, $ 824, , ,999 1, $ 7,874,166,495 $ 126,015, $ 875, , , $ 8,090,740,537 $ 216,574, $ 945,738 1,000,000-1,099, $ 8,250,203,720 $ 159,463, $ 1,049,100 1,100,000-1,199, $ 8,389,088,523 $ 138,884, $ 1,147,808 1,200,000-1,299, $ 8,488,628,328 $ 99,539, $ 1,244,248 1,300,000-1,399, $ 8,562,643,394 $ 74,015, $ 1,345,728 1,400,000-1,499, $ 8,642,022,611 $ 79,379, $ 1,443,258 1,500,000-1,599, $ 8,711,678,325 $ 69,655, $ 1,547,905 1,600,000-1,699, $ 8,749,431,846 $ 37,753, $ 1,641,457 1,700,000-1,799, $ 8,782,646,944 $ 33,215, $ 1,748,163 3
5 DISTRIBUTION OF LOSSES(All) ACCUMULATED NUMBER ACCUMULATED INDEMNITY EXCESS LIMITS CLAIMS OF LOSSES AND RATIO AVERAGE (ADDED UP) CLAIMS (ADDED DOWN) MEDICAL 1,800,000-1,899, $ 8,804,991,986 $ 22,345, $ 1,862,087 1,900,000-1,999, $ 8,830,399,796 $ 25,407, $ 1,954,447 2,000,000-2,999, $ 9,053,144,581 $ 222,744, $ 2,395,105 3,000,000-3,999, $ 9,167,720,430 $ 114,575, $ 3,471,995 4,000,000-4,999, $ 9,257,925,171 $ 90,204, $ 4,510,237 5,000,000-5,999, $ 9,279,324,638 $ 21,399, $ 5,349,867 6,000,000-6,999, $ 9,337,552,035 $ 58,227, $ 6,469,711 7,000,000-7,999, $ 9,381,565,597 $ 44,013, $ 7,335,594 8,000,000-8,999, $ 9,415,854,968 $ 34,289, $ 8,572,343 9,000,000-9,999, $ 9,425,208,307 $ 9,353, $ 9,353,339 10,000,000 - AND GREATER 1 1 $ 9,445,357,111 $ 20,148, $ 20,148,804 GRAND TOTALS 670,082 EXCLUDING CONTRACT MEDICAL $ 9,445,357,111 $ 14,096 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 9,445,357, , ,842, ,342 7,823,115,016 1, ,000 15, ,914,037 18,542 7,450,630,979 12, ,000 20, ,716,967 11,071 7,149,344,012 17, ,000 25, ,578,855 7,409 6,893,355,157 22, ,000 30, ,373,370 5,419 6,668,961,787 27, ,000 35, ,637,925 4,128 6,468,308,862 32, ,000 40, ,287,850 3,271 6,286,006,012 37, ,000 50, ,436,518 4,653 5,962,219,494 44, ,000 75, ,652,151 6,512 5,295,792,343 61, , , ,776,486 3,725 4,752,140,857 86, , , ,635,770 2,748 4,286,692, , , , ,096,100 2,229 3,884,308, , , , ,037,356 2,106 3,534,971, , , , ,459,971 1,712 3,234,711, , , , ,392,843 1,398 2,971,468, , , , ,509,840 1,136 2,741,508, , , , ,213, ,536,382, , , , ,417, ,354,678, , , , ,069, ,191,417, , , , ,630, ,045,578, , , , ,985, ,914,193, , , , ,793, ,794,033, , , , ,711, ,685,457, , , , ,481, ,586,382, , , , ,795, ,496,631, , , , ,215, ,415,197, , , , ,610, ,148,487, , , , ,104, ,882, , , , ,784, ,997, , , , ,006, ,690, , ,000 1,000, ,574, ,616, , ,000,000 2,000, ,659, ,957,315 1,286, ,000,000 3,000, ,744, ,212,530 2,395, ,000,000 4,000, ,575, ,636,681 3,471, ,000,000 5,000,000 90,204, ,431,940 4,510, ,000,000 6,000,000 21,399, ,032,473 5,349, ,000,000 7,000,000 58,227, ,805,076 6,469, ,000,000 8,000,000 44,013, ,791,514 7,335, ,000,000 9,000,000 34,289, ,502,143 8,572, ,000,000 10,000,000 9,353, ,148,804 9,353, ,000,000 & Over 20,148, ,148,804 TOTAL/AVERAGE 9,445,357, ,082 14,096 * Limits consistent with published loss limits for excess loss factors Values have been interpolated when not available on prior pages 5
7 DISTRIBUTION OF LOSSES Death-Pareto PT-Lognormal PP-Pareto TT-Pareto Actual Fitted Actual Fitted Actual Fitted Actual Fitted Loss Excess Excess Excess Excess Excess Excess Excess Excess Limit Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio 2, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
8 DISTRIBUTION OF LOSSES Death-Pareto PT-Lognormal PP-Pareto TT-Pareto Actual Fitted Actual Fitted Actual Fitted Actual Fitted Loss Excess Excess Excess Excess Excess Excess Excess Excess Limit Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio 51, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,
9 DISTRIBUTION OF LOSSES Death-Pareto PT-Lognormal PP-Pareto TT-Pareto Actual Fitted Actual Fitted Actual Fitted Actual Fitted Loss Excess Excess Excess Excess Excess Excess Excess Excess Limit Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio 120, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,000, ,100, ,200, ,300, ,400, ,500, ,600, ,700,
10 DISTRIBUTION OF LOSSES Death-Pareto PT-Lognormal PP-Pareto TT-Pareto Actual Fitted Actual Fitted Actual Fitted Actual Fitted Loss Excess Excess Excess Excess Excess Excess Excess Excess Limit Ratio Ratio Ratio Ratio Ratio Ratio Ratio Ratio 1,800, ,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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