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Journal of Statistical Distributions and Applications

Table 2 MLEs and standard deviations for various parameter values

From: The odd generalized exponential family of distributions with applications

Sample size

Actual values

Estimated values

Standard deviations

n

α

β

λ

\(\boldsymbol {\tilde {\alpha }}\)

\(\boldsymbol {\tilde {\beta }}\)

\(\boldsymbol {\tilde {\lambda }}\)

\(\boldsymbol {\tilde {\alpha }}\)

\(\boldsymbol {\tilde {\beta }}\)

\(\boldsymbol {\tilde {\lambda }}\)

100

0.5

0.5

1

0.5264

0.5493

1.0198

0.0205

0.0188

0.0284

 

0.5

1

2

0.4894

1.3254

2.1484

0.0254

0.0709

0.0461

 

0.5

1.5

1

0.5214

1.7122

1.0097

0.0249

0.0602

0.0284

 

0.5

2

2

0.4897

2.6385

2.2290

0.0252

0.1421

0.0619

 

1

0.5

1

1.0695

0.5210

1.0321

0.0429

0.0124

0.0244

 

1

1

2

1.0063

1.1701

2.0607

0.0451

0.0470

0.0327

 

1

1.5

1

1.0838

1.5895

1.0074

0.0476

0.0403

0.0267

 

1

2

2

1.0753

2.2144

2.0797

0.0538

0.0765

0.0346

 

1.5

0.5

1

1.6511

0.5250

1.0207

0.0853

0.0111

0.0264

 

1.5

1

2

1.7591

1.0921

2.0900

0.1136

0.0355

0.0323

 

1.5

1.5

1

1.6315

1.5700

1.0269

0.0670

0.0325

0.0247

 

1.5

2

2

1.7981

2.2429

2.1356

0.1037

0.1227

0.0437

300

0.5

0.5

1

0.4980

0.5261

0.9972

0.0064

0.0052

0.0086

 

0.5

1

2

0.4996

1.0557

2.0265

0.0070

0.0125

0.0111

 

0.5

1.5

1

0.5014

1.5597

0.9960

0.0066

0.0154

0.0089

 

0.5

2

2

0.4844

2.2030

2.0532

0.0079

0.0299

0.0123

 

1

0.5

1

1.0319

0.5014

1.0132

0.0130

0.0036

0.0083

 

1

1

2

0.9856

1.0539

2.0084

0.01450

0.01112

0.0097

 

1

1.5

1

1.0277

1.5324

1.0063

0.0127

0.0116

0.0079

 

1

2

2

1.0053

2.0929

2.0217

0.01536

0.0216

0.0097

 

1.5

0.5

1

1.5457

0.5078

1.0068

0.0182

0.0038

0.0077

 

1.5

1

2

1.5414

1.0310

2.0300

0.0250

0.0096

0.0094

 

1.5

1.5

1

1.5356

1.5182

1.0085

0.0185

0.0098

0.0077

 

1.5

2

2

1.5377

2.0670

2.0177

0.02377

0.02022

0.0085

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