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Journal of Statistical Distributions and Applications

Table 3 Performance of the MLEs for the ℳOG 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)

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