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Table 4 Numerical results for different sites and various approaches

From: Optimization of the distribution of wind speeds using convexly combined Weibull densities

 

Site 1

Site 2

Site 3

Weibull PDF

   

 k

1.459

2.947

2.436

 c

4.044

4.474

5.688

 KS test statistic value

0.084

0.089

0.091

Bimodal Weibull PDF

   

 \(\lambda _1\)

0.002

0.397

0.070

 \(k_1\)

1.294

5.451

2.310

 \(c_1\)

50.000

3.114

10.095

 \(\lambda _2\)

0.998

0.603

0.930

 \(k_2\)

1.869

3.789

3.521

 \(c_2\)

4.023

5.222

5.299

 KS test statistic value

0.051

0.035

0.019

Gamma–Weibull PDF

   

 \(\lambda _1\)

0.765

0.514

0.979

 \(\alpha \)

3.353

15.843

8.344

 \(\beta \)

1.268

0.194

0.586

 \(\lambda _2\)

0.235

0.486

0.022

 k

3.351

4.076

3.746

 c

1.852

5.462

14.424

 KS test statistic value

0.079

0.025

0.020

Convexly combined Weibull PDF

   

 \(\lambda _1\)

0.000

0.039

0.065

 \(k_1\)

3.400

9.134

11.811

 \(c_1\)

10.644

6.812

5.666

 \(\lambda _2\)

0.311

0.021

0.100

 \(k_2\)

3.229

6.800

4.251

 \(c_2\)

3.044

3.409

7.414

 \(\lambda _3\)

0.018

0.000

0.087

 \(k_3\)

3.523

1.000

5.551

 \(c_3\)

2.733

5.773

3.165

 \(\lambda _4\)

0.160

0.011

0.052

 \(k_4\)

5.669

12.425

4.891

 \(c_4\)

6.523

7.931

2.612

 \(\lambda _5\)

0.010

0.032

0.045

 \(k_5\)

3.525

18.863

18.392

 \(c_5\)

5.607

4.731

4.921

 \(\lambda _6\)

0.002

0.148

0.000

 \(k_6\)

1.289

9.826

1.000

 \(c_6\)

50.000

3.949

3.081

 \(\lambda _7\)

0.001

0.047

0.121

 \(k_7\)

2.405

5.713

4.676

 \(c_7\)

11.741

5.077

5.114

 \(\lambda _8\)

0.186

0.000

0.005

 \(k_8\)

5.608

2.828

19.063

 \(c_8\)

5.772

4.997

11.806

 \(\lambda _9\)

0.274

0.302

0.358

 \(k_9\)

3.214

6.298

5.062

 \(c_9\)

1.806

2.736

5.980

 \(\lambda _{10}\)

0.019

0.082

0.025

 \(k_{10}\)

2.827

14.432

3.242

 \(c_{10}\)

3.512

3.365

13.675

 \(\lambda _{11}\)

0.000

0.000

0.139

 \(k_{11}\)

4.720

5.270

9.266

 \(c_{11}\)

6.344

4.508

4.048

 \(\lambda _{12}\)

0.020

0.319

0.004

 \(k_{12}\)

26.295

5.217

4.399

 \(c_{12}\)

7.201

5.553

5.338

 KS test statistic value

0.017

0.024

0.012