Table 2.
Means of estimates of the parameters and MSEs (in parentheses) for many estimation methods when n = 30.
| n | α | β | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 30 | 0.75 | 0.75 | 0.8248 | 0.8421 | 0.8131 | 0.8093 | 0.7648 | 0.7694 | 0.7743 | 0.7838 | 0.7355 | 0.707 | 0.7602 | 0.7459 | 0.7835 | 0.797 | 0.8021 | 0.8734 |
| (0.0346) | (0.0686) | (0.0294) | (0.0520) | (0.0388) | (0.0871) | (0.0344) | (0.0759) | (0.0213) | (0.0464) | (0.0472) | (0.0759) | (0.0322) | (0.0647) | (0.0380) | (0.1732) | |||
| 1.5 | 0.8326 | 1.6937 | 0.8329 | 1.6944 | 0.7663 | 1.5435 | 0.7779 | 1.578 | 0.7432 | 1.4237 | 0.7588 | 1.465 | 0.7873 | 1.6026 | 0.8084 | 1.77 | ||
| (0.0354) | (0.2803) | (0.0323) | (0.2233) | (0.0384) | (0.3497) | (0.0336) | (0.3079) | (0.0207) | (0.1859) | (0.0499) | (0.2286) | (0.0322) | (0.2621) | (0.0381) | (0.7220) | |||
| 2.5 | 0.8409 | 2.8462 | 0.8214 | 2.6558 | 0.7682 | 2.5903 | 0.7822 | 2.6579 | 0.7514 | 2.3954 | 0.7545 | 2.4078 | 0.7917 | 2.6935 | 0.8147 | 2.9966 | ||
| (0.0363) | (0.7761) | (0.0280) | (0.4083) | (0.0366) | (0.9924) | (0.0317) | (0.8855) | (0.0202) | (0.4971) | (0.0565) | (0.6103) | (0.0318) | (0.7327) | (0.0376) | (2.1468) | |||
| 1.5 | 0.75 | 1.6323 | 0.8032 | 1.548 | 0.7687 | 1.5357 | 0.7525 | 1.551 | 0.7624 | 1.4179 | 0.7005 | 1.5055 | 0.7427 | 1.5678 | 0.7725 | 1.5955 | 0.7977 | |
| (0.1813) | (0.0335) | (0.1171) | (0.0254) | (0.2034) | (0.0403) | (0.1823) | (0.0357) | (0.1197) | (0.0270) | (0.1701) | (0.0473) | (0.1666) | (0.0322) | (0.1978) | (0.0548) | |||
| 1.5 | 1.6316 | 1.6031 | 1.5746 | 1.5803 | 1.5358 | 1.5019 | 1.5508 | 1.5215 | 1.417 | 1.3978 | 1.5052 | 1.4717 | 1.5667 | 1.5417 | 1.5966 | 1.5943 | ||
| (0.1820) | (0.1357) | (0.1234) | (0.1059) | (0.2152) | (0.1603) | (0.1917) | (0.1425) | (0.1200) | (0.1110) | (0.1660) | (0.1266) | (0.1683) | (0.1294) | (0.2029) | (0.2169) | |||
| 2.5 | 1.6357 | 2.6806 | 1.5395 | 2.5318 | 1.5361 | 2.5089 | 1.5515 | 2.5421 | 1.4208 | 2.338 | 1.4957 | 2.427 | 1.569 | 2.5766 | 1.5975 | 2.6627 | ||
| (0.1810) | (0.3730) | (0.1086) | (0.2333) | (0.2034) | (0.4479) | (0.1822) | (0.3968) | (0.1182) | (0.2992) | (0.1764) | (0.3265) | (0.1666) | (0.3584) | (0.1977) | (0.6098) | |||
| 2.5 | 0.75 | 2.7646 | 0.7917 | 2.7206 | 0.7784 | 2.5881 | 0.7479 | 2.6136 | 0.7566 | 2.341 | 0.7019 | 2.4773 | 0.7306 | 2.6389 | 0.7649 | 2.6989 | 0.7826 | |
| (0.6938) | (0.0246) | (0.4343) | (0.0193) | (0.8772) | (0.0290) | (0.7596) | (0.0257) | (0.4181) | (0.0212) | (0.6223) | (0.0390) | (0.6241) | (0.0234) | (0.7769) | (0.0340) | |||
| 1.5 | 2.7649 | 1.5835 | 2.7689 | 1.5904 | 2.5882 | 1.4958 | 2.6137 | 1.5132 | 2.3413 | 1.4038 | 2.486 | 1.468 | 2.6392 | 1.5299 | 2.6992 | 1.5653 | ||
| (0.6939) | (0.0985) | (0.4657) | (0.0804) | (0.8773) | (0.1160) | (0.7596) | (0.1030) | (0.4178) | (0.0847) | (0.4900) | (0.0922) | (0.6242) | (0.0937) | (0.7770) | (0.1359) | |||
| 2.5 | 2.7706 | 2.6458 | 2.7033 | 2.576 | 2.5877 | 2.4973 | 2.6141 | 2.5268 | 2.3466 | 2.3462 | 2.4768 | 2.4326 | 2.6432 | 2.5553 | 2.6991 | 2.6119 | ||
| (0.6900) | (0.2715) | (0.4012) | (0.1828) | (0.8102) | (0.3223) | (0.7091) | (0.2850) | (0.4132) | (0.2295) | (0.4893) | (0.2311) | (0.6191) | (0.2591) | (0.7557) | (0.3790) |