TESTS OF FUNCTIONS TO FIND THE MLE FOR THE POISSON MODEL WITHOUT ZEROS. > n<-c(1,2,1,1,3) > nzp.simple.iteration(n,15) lambda log.lik 1 1.600000 -3.112386 2 1.276966 -2.794171 3 1.153788 -2.729644 4 1.095297 -2.712646 5 1.064895 -2.707666 6 1.048378 -2.706129 7 1.039191 -2.705642 8 1.034015 -2.705485 9 1.031077 -2.705434 10 1.029404 -2.705418 11 1.028448 -2.705412 12 1.027902 -2.705411 13 1.027589 -2.705410 14 1.027410 -2.705410 15 1.027308 -2.705410 16 1.027249 -2.705410 > nzp.simple.iteration(n,15,0.1) lambda log.lik 1 0.1000000 -7.159838 2 0.1522601 -6.031974 3 0.2259762 -5.037551 4 0.3236207 -4.215401 5 0.4423606 -3.593492 6 0.5719713 -3.173899 7 0.6969413 -2.926302 8 0.8030295 -2.799296 9 0.8832484 -2.742050 10 0.9384996 -2.718835 11 0.9740570 -2.710123 12 0.9959229 -2.707020 13 1.0089882 -2.705951 14 1.0166597 -2.705590 15 1.0211177 -2.705469 16 1.0236926 -2.705429 > nzp.simple.iteration(n,15,10) lambda log.lik 1 10.000000 -31.579092 2 1.599927 -3.112294 3 1.276942 -2.794155 4 1.153778 -2.729641 5 1.095292 -2.712645 6 1.064893 -2.707666 7 1.048376 -2.706129 8 1.039190 -2.705642 9 1.034014 -2.705485 10 1.031077 -2.705434 11 1.029404 -2.705418 12 1.028448 -2.705412 13 1.027902 -2.705411 14 1.027589 -2.705410 15 1.027410 -2.705410 16 1.027308 -2.705410 > nzp.newton.raphson(n,15) lambda log.lik 1 1.6000000 -3.112386 2 0.7787627 -2.822769 3 0.9714403 -2.710607 4 1.0244661 -2.705422 5 1.0271638 -2.705410 6 1.0271701 -2.705410 7 1.0271701 -2.705410 8 1.0271701 -2.705410 9 1.0271701 -2.705410 10 1.0271701 -2.705410 11 1.0271701 -2.705410 12 1.0271701 -2.705410 13 1.0271701 -2.705410 14 1.0271701 -2.705410 15 1.0271701 -2.705410 16 1.0271701 -2.705410 > nzp.newton.raphson(n,15,0.1) lambda log.lik 1 0.1000000 -7.159838 2 0.1914009 -5.446287 3 0.3504920 -4.047049 4 0.5886078 -3.133477 5 0.8480668 -2.763504 6 0.9985621 -2.706757 7 1.0264615 -2.705411 8 1.0271697 -2.705410 9 1.0271701 -2.705410 10 1.0271701 -2.705410 11 1.0271701 -2.705410 12 1.0271701 -2.705410 13 1.0271701 -2.705410 14 1.0271701 -2.705410 15 1.0271701 -2.705410 16 1.0271701 -2.705410 > nzp.newton.raphson(n,15,10) lambda log.lik 1 10.00000 -31.57909 2 -42.65225 NaN 3 -85.30450 NaN 4 -170.60901 NaN 5 -341.21801 NaN 6 -682.43603 NaN 7 -1364.87206 NaN 8 NaN NaN 9 NaN NaN 10 NaN NaN 11 NaN NaN 12 NaN NaN 13 NaN NaN 14 NaN NaN 15 NaN NaN 16 NaN NaN Warning messages: 1: NaNs produced in: log(x) 2: NaNs produced in: log(x) > nzp.method.of.scoring(n,15) lambda log.lik 1 1.600000 -3.112386 2 1.057311 -2.706856 3 1.027271 -2.705410 4 1.027170 -2.705410 5 1.027170 -2.705410 6 1.027170 -2.705410 7 1.027170 -2.705410 8 1.027170 -2.705410 9 1.027170 -2.705410 10 1.027170 -2.705410 11 1.027170 -2.705410 12 1.027170 -2.705410 13 1.027170 -2.705410 14 1.027170 -2.705410 15 1.027170 -2.705410 16 1.027170 -2.705410 > nzp.method.of.scoring(n,15,0.1) lambda log.lik 1 0.100000 -7.159838 2 1.162915 -2.733133 3 1.029150 -2.705416 4 1.027171 -2.705410 5 1.027170 -2.705410 6 1.027170 -2.705410 7 1.027170 -2.705410 8 1.027170 -2.705410 9 1.027170 -2.705410 10 1.027170 -2.705410 11 1.027170 -2.705410 12 1.027170 -2.705410 13 1.027170 -2.705410 14 1.027170 -2.705410 15 1.027170 -2.705410 16 1.027170 -2.705410 > nzp.method.of.scoring(n,15,10) lambda log.lik 1 10.000000 -31.579092 2 1.596112 -3.107480 3 1.056944 -2.706821 4 1.027269 -2.705410 5 1.027170 -2.705410 6 1.027170 -2.705410 7 1.027170 -2.705410 8 1.027170 -2.705410 9 1.027170 -2.705410 10 1.027170 -2.705410 11 1.027170 -2.705410 12 1.027170 -2.705410 13 1.027170 -2.705410 14 1.027170 -2.705410 15 1.027170 -2.705410 16 1.027170 -2.705410 > n<-c(1,2,1,1,1) > nzp.simple.iteration(n,15) lambda log.lik 1 1.2000000 -3.114159 2 0.8385669 -2.418128 3 0.6812044 -2.183208 4 0.5927914 -2.077887 5 0.5366615 -2.023899 6 0.4983636 -1.993971 7 0.4709712 -1.976512 8 0.4507253 -1.965963 9 0.4354010 -1.959423 10 0.4235938 -1.955291 11 0.4143723 -1.952642 12 0.4070941 -1.950925 13 0.4013021 -1.949802 14 0.3966627 -1.949062 15 0.3929270 -1.948573 16 0.3899063 -1.948247 > nzp.simple.iteration(n,15,0.1) lambda log.lik 1 0.1000000 -2.554668 2 0.1141951 -2.458051 3 0.1294993 -2.371321 4 0.1457578 -2.294629 5 0.1627595 -2.227898 6 0.1802454 -2.170816 7 0.1979217 -2.122846 8 0.2154791 -2.083259 9 0.2326138 -2.051178 10 0.2490486 -2.025644 11 0.2645495 -2.005673 12 0.2789380 -1.990310 13 0.2920958 -1.978675 14 0.3039636 -1.969990 15 0.3145347 -1.963591 16 0.3238458 -1.958932 > nzp.simple.iteration(n,15,10) lambda log.lik 1 10.0000000 -36.184262 2 1.1999455 -3.114041 3 0.8385473 -2.418096 4 0.6811942 -2.183194 5 0.5927852 -2.077880 6 0.5366574 -2.023896 7 0.4983607 -1.993969 8 0.4709691 -1.976511 9 0.4507237 -1.965962 10 0.4353998 -1.959422 11 0.4235929 -1.955290 12 0.4143715 -1.952642 13 0.4070935 -1.950925 14 0.4013017 -1.949802 15 0.3966623 -1.949062 16 0.3929267 -1.948573 > nzp.newton.raphson(n,15) lambda log.lik 1 1.2000000 -3.114159 2 -0.7903745 NaN 3 -2.5059333 NaN 4 -6.6397071 NaN 5 -13.5648162 NaN 6 -27.1321084 NaN 7 -54.2642168 NaN 8 -108.5284336 NaN 9 -217.0568672 NaN 10 -434.1137344 NaN 11 -868.2274687 NaN 12 NaN NaN 13 NaN NaN 14 NaN NaN 15 NaN NaN 16 NaN NaN Warning messages: 1: NaNs produced in: log(x) 2: NaNs produced in: log(x) > nzp.newton.raphson(n,15,0.1) lambda log.lik 1 0.1000000 -2.554668 2 0.1742741 -2.189137 3 0.2692156 -2.000372 4 0.3467844 -1.951042 5 0.3742121 -1.947603 6 0.3764256 -1.947584 7 0.3764380 -1.947584 8 0.3764380 -1.947584 9 0.3764380 -1.947584 10 0.3764380 -1.947584 11 0.3764380 -1.947584 12 0.3764380 -1.947584 13 0.3764380 -1.947584 14 0.3764380 -1.947584 15 0.3764380 -1.947584 16 0.3764380 -1.947584 > nzp.newton.raphson(n,15,10) lambda log.lik 1 10.00000 -36.18426 2 -63.61565 NaN 3 -127.23131 NaN 4 -254.46262 NaN 5 -508.92523 NaN 6 -1017.85047 NaN 7 NaN NaN 8 NaN NaN 9 NaN NaN 10 NaN NaN 11 NaN NaN 12 NaN NaN 13 NaN NaN 14 NaN NaN 15 NaN NaN 16 NaN NaN Warning messages: 1: NaNs produced in: log(x) 2: NaNs produced in: log(x) > nzp.method.of.scoring(n,15) lambda log.lik 1 1.2000000 -3.114159 2 0.4513577 -1.966260 3 0.3772372 -1.947587 4 0.3764381 -1.947584 5 0.3764380 -1.947584 6 0.3764380 -1.947584 7 0.3764380 -1.947584 8 0.3764380 -1.947584 9 0.3764380 -1.947584 10 0.3764380 -1.947584 11 0.3764380 -1.947584 12 0.3764380 -1.947584 13 0.3764380 -1.947584 14 0.3764380 -1.947584 15 0.3764380 -1.947584 16 0.3764380 -1.947584 > nzp.method.of.scoring(n,15,0.1) lambda log.lik 1 0.1000000 -2.554668 2 0.3887130 -1.948136 3 0.3764599 -1.947584 4 0.3764380 -1.947584 5 0.3764380 -1.947584 6 0.3764380 -1.947584 7 0.3764380 -1.947584 8 0.3764380 -1.947584 9 0.3764380 -1.947584 10 0.3764380 -1.947584 11 0.3764380 -1.947584 12 0.3764380 -1.947584 13 0.3764380 -1.947584 14 0.3764380 -1.947584 15 0.3764380 -1.947584 16 0.3764380 -1.947584 > nzp.method.of.scoring(n,15,10) lambda log.lik 1 10.0000000 -36.184262 2 1.1959483 -3.105436 3 0.4507237 -1.965962 4 0.3772239 -1.947586 5 0.3764381 -1.947584 6 0.3764380 -1.947584 7 0.3764380 -1.947584 8 0.3764380 -1.947584 9 0.3764380 -1.947584 10 0.3764380 -1.947584 11 0.3764380 -1.947584 12 0.3764380 -1.947584 13 0.3764380 -1.947584 14 0.3764380 -1.947584 15 0.3764380 -1.947584 16 0.3764380 -1.947584