δ
0.025 0.05 0.075 0.1
π π π π
N   0.025 0.05 0.075 0.1 0.025 0.05 0.075 0.1 0.025 0.05 0.075 0.1 0.025 0.05 0.075 0.1
10 RB  0.02947 0.02258 0.04016 0.03863 0.13102 0.07173 0.09012 0.06763 0.24288 0.12071 0.11051 0.10479 0.33570 0.18675 0.14564 0.15245
RBE 0.03021 0.02474 0.04221 0.04513 0.12475 0.07008 0.09192 0.07777 0.22789 0.11552 0.10892 0.11093 0.31133 0.16957 0.13704 0.15162
RMSE        0.99578 0.98579 0.99114 0.90046 1.01075 1.02702 1.00010 0.92797 1.04519 1.01203 1.04029 0.95725 1.04125 1.06464 1.04087 1.01525
30 RB  0.00802 0.01036 0.01316 0.00871 0.03736 0.01877 0.01972 0.01997 0.06229 0.03655 0.02350 0.03446 0.08924 0.06558 0.06124 0.03677
RBE 0.00778 0.01194 0.01684 0.01474 0.03303 0.01777 0.02252 0.02682 0.05223 0.03117 0.02224 0.03797 0.07198 0.05321 0.05455 0.03376
RMSE        1.00309 0.98850 0.96432 0.93459 1.02808 1.00170 0.99492 0.95885 1.04456 1.04185 1.02271 1.00198 1.08761 1.08077 1.03345 1.05222
50 RB  0.01008 0.00247 0.00309 0.00439 0.01118 0.01067 0.01058 0.00521 0.03868 0.01866 0.02416 0.01035 0.06565 0.03432 0.03297 0.03320
RBE 0.00997 0.00401 0.00688 0.01069 0.00796 0.01036 0.01337 0.01225 0.03002 0.01382 0.02270 0.01336 0.04995 0.02394 0.02592 0.03031
RMSE        1.00058 0.98683 0.96670 0.93616 1.01788 1.00520 0.99666 0.96695 1.04735 1.03331 1.01907 1.01246 1.07330 1.05838 1.05647 1.04896
100 RB  0.00395 0.00342 -0.00092 -0.00203 0.00787 0.00838 0.00384 0.00221 0.01871 0.01858 0.01445 0.00792 0.04271 0.02876 0.01196 0.01248
RBE 0.00383 0.00502 0.00295 0.00423 0.00494 0.00790 0.00697 0.00957 0.01080 0.01356 0.01322 0.01130 0.02889 0.01841 0.00537 0.01005
RMSE        1.00121 0.98672 0.96740 0.94398 1.02159 1.00838 0.98715 0.96012 1.04804 1.03945 1.01994 1.00181 1.08931 1.06980 1.05148 1.04374
200 RB  -0.00134 -0.00086 -0.00197 -0.00718 0.00898 -0.00057 -0.00191 -0.00822 0.01747 0.01051 0.00419 0.00133 0.02724 0.01607 0.00991 0.00703
RBE -0.00140 0.00076 0.00195 -0.00099 0.00610 -0.00095 0.00124 -0.00086 0.01031 0.00597 0.00307 0.00454 0.01496 0.00642 0.00388 0.00483
RMSE        1.00082 0.98763 0.96873 0.95629 1.02283 1.00717 0.99031 0.97972 1.05062 1.03692 1.02093 1.00423 1.08130 1.06762 1.05158 1.03280
Table 2: Relative bias (RB) and relative mean squared error (RMSE) for the beta-binomial model and Relative bias (RBE) for the exact distribution (Equation 3), using various combinations of π, δ and N with k=25 and nl=10, l=1,2,…,N.