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Table 3 Performance of the MLEs for the OG distribution

From: The Marshall-Olkin extended Weibull family of distributions

( α, δ, β) n θ ̂ i ¯ (MSE( θ ̂ i ))
   α ̂ ¯ (MSE ( α ̂ )) δ ̂ ¯ (MSE ( δ ̂ )) β ̂ ¯ (MSE ( β ̂ ))
For η<1
(1,0.3,2) 50 1.201 (2.837) 0.478 (0.883) 2.502 (1.698)
· 100 1.181 (1.745) 0.406 (0.290) 2.320 (1.238)
· 150 1.156 (1.299) 0.385 (0.195) 2.249 (1.015)
· 200 1.103 (1.008) 0.358 (0.134) 2.244 (0.899)
(1,1,2) 50 1.202 (1.965) 1.620 (5.938) 2.425 (1.630)
· 100 1.134 (1.199) 1.361 (2.690) 2.305 (1.145)
· 150 1.079 (0.884) 1.231 (1.638) 2.288 (0.979)
· 200 1.063 (0.735) 1.180 (1.244) 2.250 (0.845)
(1,4,2) 50 0.965 (0.810) 4.764 (26.798) 2.544 (1.561)
· 100 0.958 (0.544) 4.398 (14.813) 2.390 (1.025)
· 150 0.959 (0.443) 4.283 (11.454) 2.328 (0.831)
· 200 0.970 (0.369) 4.246 (8.953) 2.262 (0.653)
For η=1
(2,0.3,2) 50 2.246 (7.571) 0.426 (0.473) 2.787 (3.543)
· 100 2.137 (4.502) 0.361 (0.172) 2.561 (2.473)
· 150 2.073 (3.279) 0.341 (0.116) 2.471 (1.981)
· 200 2.011 (2.596) 0.324 (0.083) 2.434 (1.698)
(2,1,2) 50 2.161 (5.462) 1.481 (4.886) 2.687 (3.051)
· 100 2.012 (3.115) 1.199 (1.798) 2.543 (2.157)
· 150 1.947 (2.277) 1.100 (1.062) 2.483 (1.763)
· 200 1.923 (1.874) 1.056 (0.787) 2.430 (1.507)
(2,4,2) 50 1.805 (2.404) 4.534 (21.279) 2.785 (2.783)
· 100 1.817 (1.681) 4.202 (12.456) 2.572 (1.869)
· 150 1.828 (1.390) 4.097 (9.474) 2.487 (1.527)
· 200 1.861 (1.153) 4.075 (7.495) 2.388 (1.184)
For η>1
(4,0.3,2) 50 3.770 (13.137) 0.336 (0.191) 3.400 (6.701)
· 100 3.737 (8.129) 0.304 (0.072) 2.951 (4.152)
· 150 3.731 (6.119) 0.298 (0.051) 2.764 (3.184)
· 200 3.685 (4.865) 0.289 (0.038) 2.676 (2.613)
(4,1,2) 50 3.845 (13.615) 1.272 (3.153) 3.149 (6.239)
· 100 3.735 (7.757) 1.076 (1.043) 2.833 (4.060)
· 150 3.717 (5.760) 1.024 (0.634) 2.689 (3.150)
· 200 3.721 (4.759) 1.000 (0.472) 2.588 (2.601)
(4,4,2) 50 3.608 (8.172) 4.605 (21.140) 3.036 (5.150)
· 100 3.677 (5.234) 4.262 (11.467) 2.668 (2.989)
· 150 3.737 (4.039) 4.172 (8.228) 2.510 (2.169)
· 200 3.796 (3.247) 4.138 (6.370) 2.389 (1.588)