Table 3.
Means of estimates of the parameters and MSEs (in parentheses) for many estimation methods when n = 100.
| n | α | β | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 100 | 0.75 | 0.75 | 0.7905 | 0.7879 | 0.7879 | 0.7795 | 0.7551 | 0.7564 | 0.7661 | 0.7711 | 0.7583 | 0.7369 | 0.7538 | 0.7499 | 0.7645 | 0.7692 | 0.7724 | 0.7955 |
| (0.0084) | (0.0155) | (0.0080) | (0.0142) | (0.0092) | (0.0203) | (0.0076) | (0.0170) | (0.0060) | (0.0126) | (0.0132) | (0.0228) | (0.0079) | (0.0161) | (0.0085) | (0.0301) | |||
| 1.5 | 0.7987 | 1.5852 | 0.7999 | 1.5907 | 0.7566 | 1.5168 | 0.7723 | 1.5564 | 0.7669 | 1.4838 | 0.753 | 1.4901 | 0.7681 | 1.546 | 0.7784 | 1.6105 | ||
| (0.0090) | (0.0639) | (0.0090) | (0.0613) | (0.0092) | (0.0816) | (0.0074) | (0.0700) | (0.0061) | (0.0508) | (0.0142) | (0.0661) | (0.0079) | (0.0653) | (0.0087) | (0.1264) | |||
| 2.5 | 0.8043 | 2.6443 | 0.7996 | 2.5979 | 0.7569 | 2.528 | 0.7776 | 2.6104 | 0.7728 | 2.4764 | 0.7455 | 2.4468 | 0.7702 | 2.5801 | 0.7832 | 2.7096 | ||
| (0.0095) | (0.1725) | (0.0087) | (0.1414) | (0.0091) | (0.2218) | (0.0074) | (0.1949) | (0.0062) | (0.1360) | (0.0154) | (0.1638) | (0.0080) | (0.1780) | (0.0090) | (0.3627) | |||
| 1.5 | 0.75 | 1.5333 | 0.7633 | 1.513 | 0.7541 | 1.505 | 0.7484 | 1.5138 | 0.7537 | 1.4519 | 0.7236 | 1.4986 | 0.746 | 1.515 | 0.7545 | 1.5222 | 0.7613 | |
| (0.0368) | (0.0080) | (0.0331) | (0.0074) | (0.0474) | (0.0105) | (0.0406) | (0.0089) | (0.0333) | (0.0079) | (0.0484) | (0.0142) | (0.0394) | (0.0086) | (0.0432) | (0.0127) | |||
| 1.5 | 1.5375 | 1.5289 | 1.5258 | 1.5252 | 1.5073 | 1.4979 | 1.5165 | 1.509 | 1.4559 | 1.4494 | 1.5002 | 1.4894 | 1.5179 | 1.5108 | 1.5244 | 1.5234 | ||
| (0.0366) | (0.0323) | (0.0333) | (0.0302) | (0.0469) | (0.0421) | (0.0402) | (0.0359) | (0.0324) | (0.0314) | (0.0454) | (0.0377) | (0.0388) | (0.0346) | (0.0420) | (0.0496) | |||
| 2.5 | 1.5395 | 2.5536 | 1.5159 | 2.5139 | 1.5074 | 2.4993 | 1.5168 | 2.5184 | 1.4581 | 2.4214 | 1.4934 | 2.4698 | 1.5181 | 2.5209 | 1.5255 | 2.5446 | ||
| (0.0366) | (0.0897) | (0.0320) | (0.0784) | (0.0476) | (0.1176) | (0.0405) | (0.0989) | (0.0321) | (0.0859) | (0.0493) | (0.0952) | (0.0393) | (0.0958) | (0.0430) | (0.1430) | |||
| 2.5 | 0.75 | 2.5698 | 0.762 | 2.5745 | 0.7598 | 2.5163 | 0.7483 | 2.5346 | 0.7535 | 2.4107 | 0.7271 | 2.4819 | 0.7417 | 2.5364 | 0.7541 | 2.5475 | 0.7581 | |
| (0.1280) | (0.0061) | (0.1183) | (0.0057) | (0.1686) | (0.0078) | (0.1411) | (0.0067) | (0.1121) | (0.0060) | (0.1507) | (0.0113) | (0.1350) | (0.0064) | (0.1449) | (0.0083) | |||
| 1.5 | 2.573 | 1.5252 | 2.5928 | 1.5315 | 2.5185 | 1.4979 | 2.5371 | 1.5084 | 2.4136 | 1.4552 | 2.492 | 1.4893 | 2.5384 | 1.5093 | 2.551 | 1.5179 | ||
| (0.1286) | (0.0248) | (0.1223) | (0.0238) | (0.1674) | (0.0315) | (0.1410) | (0.0270) | (0.1116) | (0.0244) | (0.1283) | (0.0278) | (0.1345) | (0.0260) | (0.1461) | (0.0341) | |||
| 2.5 | 2.5633 | 2.5348 | 2.5622 | 2.5211 | 2.513 | 2.4925 | 2.5292 | 2.5082 | 2.4046 | 2.4185 | 2.4778 | 2.4683 | 2.5312 | 2.5101 | 2.5452 | 2.5257 | ||
| (0.1279) | (0.0668) | (0.1148) | (0.0603) | (0.1702) | (0.0868) | (0.1425) | (0.0737) | (0.1136) | (0.0674) | (0.1337) | (0.0689) | (0.1368) | (0.0713) | (0.1497) | (0.0946) |