Table 20 Estimated parameter values of the PC-JD, calculated through multiple estimation approaches utilizing the RSS second dataset.

From: Optimal estimation of power Chris-Jerry distribution parameters using ranked set sampling design with application

Method

\(s=5\)

\(w=3\)

\(s=5\)

\(w=6\)

\(s=5\)

\(w=9\)

\(s=5\)

\(w=12\)

\(\hat{\beta }\)

\(\hat{\alpha }\)

\(\hat{\beta }\)

\(\hat{\alpha }\)

\(\hat{\beta }\)

\(\hat{\alpha }\)

\(\hat{\beta }\)

\(\hat{\alpha }\)

ML

0.5114

0.7726

0.6339

0.7134

0.5401

0.7830

0.6541

0.6698

OLS

0.5168

0.7582

0.6877

0.6669

0.6500

0.6861

0.6819

0.6431

WLS

0.5559

0.7295

0.6570

0.6896

0.5612

0.7592

0.6565

0.6656

CVM

0.4644

0.8269

0.6252

0.7222

0.5379

0.7861

0.6361

0.6847

MPS

0.6305

0.6558

0.6904

0.6526

0.5572

0.7600

0.6573

0.6660

AD

0.5246

0.7586

0.6474

0.7007

0.5500

0.7722

0.6705

0.6574

RTAD

0.4973

0.7861

0.6811

0.6749

0.5831

0.7430

0.6471

0.6742

LTAD

0.5432

0.7328

0.6188

0.7399

0.5177

0.8204

0.6848

0.6412

MSAD

0.8577

0.5265

0.8444

0.5399

0.6176

0.7454

0.6827

0.6619

MSALD

0.7029

0.5866

0.6181

0.6271

0.5693

0.7713

0.5126

0.7445

MSSD

0.8067

0.5783

0.6730

0.6582

0.6217

0.6905

0.5734

0.6879

MSSLDD

0.5356

0.7082

0.6072

0.6474

0.6063

0.7059

0.4575

0.7893

MSLND

0.8024

0.5830

0.6716

0.6595

0.6227

0.6896

0.5728

0.6881

KE

0.3957

0.8919

0.5964

0.7680

0.5666

0.7711

0.7015

0.6437

ADSO

0.5810

0.6892

0.5643

0.8333

0.4545

0.9385

0.6820

0.6475

PC

0.7018

0.6166

0.8667

0.5586

0.5742

0.7438

0.6110

0.6965

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