First Step: Calculation of Basic Variance Parameters I. Sum of Squared Differences from Sample Means Within Classes "$$i$$" = $$\alpha^2$$ = 7.379E+9 II. Sum of Exposures Times Squared Differences Between Class Sample Means "$$L_i$$'s" and Overall Mean "$$M$$" = $$\beta^2$$ = 3.941E+8 III. = I./((total(1)-15(="$$n$$"))=Process Variance = $$s^2$$ = 4,131,869 IV. = [II.- ($$n$$-1.0)III.]/[total(1)-$$\sum_{i=1}^{15}e_i^2$$/total(1)]= Variance of Hypothetical Means = $$\sigma^2$$ = 208,304 V. III./IV = Credibility Constant=$$K$$ = 19.84 Second Step: Main Calculations for Class Rates (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) $$i$$ $$e_i$$ $$l_i$$ $$L_i$$ $$Z_i$$ $$Z_iL_i+(1-Z_i)M$$ $$[Z_iL_i+(1-Z_i)M]\times e_i$$ $$e_i(1-Z_i)$$ $$e_i(1-Z_i)M\times C$$ $$e_i\times r_i]$$ $$final \ r_i$$ (Data) (Data) (1)/(2) (1)/((1)+V.) (3)$$\times$$(4)​+A$$\times$$(1.0-(4)) (5)$$\times$$(1) (1) $$\times$$ (1.0-(4)) (7)$$\times$$A$$\times$$F (6)+(8) (5)$$\times$$(9)/(1) Class Exposure Losses Raw Rate "l" Credibility of Class Credibility Adjusted Rate Losses in Adjusted Rates Off-Balance Correction Basis Additional Losses From Off-Balance Correction Off-Balance Corrected Total Losses Off-Balance Corrected (Rate 1 25 $78,427$ 3,137 56 % $1,978$ 49,456 $11$ 3,162 $52,617$ 2,105 2 30 $40,687$ 1,356 60 % $1,022$ 30,674 $12$ 3,413 $34,087$ 1,136 3 36 $65,073$ 1,808 64 % $1,349$ 48,576 $13$ 3,656 $52,232$ 1,451 4 43 $35,837$ 830 69 % $731$ 31,596 $14$ 3,886 $35,482$ 821 5 52 $59,918$ 1,156 72 % $979$ 50,762 $14$ 4,101 $54,863$ 1,058 6 62 $72,435$ 1,164 76 % $1,008$ 62,708 $15$ 4,299 $67,007$ 1,077 7 75 $63,990$ 857 79 % $786$ 58,669 $16$ 4,480 $63,149$ 846 8 90 $57,059$ 637 82 % $615$ 55,121 $16$ 4,642 $59,764$ 667 9 107 $90,110$ 838 84 % $788$ 84,741 $17$ 4,787 $89,528$ 833 10 129 $46,934$ 364 87 % $384$ 49,578 $17$ 4,914 $54,492$ 422 11 155 $47,281$ 305 89 % $330$ 51,012 $18$ 5,026 $56,038$ 362 12 186 $54,427$ 293 90 % $315$ 58,453 $18$ 5,123 $63,576$ 342 13 223 $69,726$ 313 92 % $330$ 73,457 $18$ 5,207 $78,664$ 353 14 267 $64,108$ 240 93 % $259$ 69,241 $18$ 5,279 $74,520$ 279 15 321 $86,197$ 269 94 % $283$ 90,850 $19$ 5,340 $96,191$ 300 Total 1,801 $932,211$ 518 $480$ 864,895 $235$ 67,315 $932,211$ 518 Reference Values for All Classes A = Overall Average Rate $518 B = Total Loss in Credibility Adjusted Rates$ 864,895 C= Total Losses in Data $932,211 D = C-B = Shortfall$ 67,315 E =Total Off-Balance Correction Basis \$ 235 F = D/E = Off-Balance Factor 285.86