Table 2 A summary of moments of the EAPLL distribution for different parameter combinations \((\beta , \lambda , \theta , \alpha )\).

From: Properties, estimation, and applications of the extended log-logistic distribution

\(\beta \)

\(\lambda \)

\(\theta \)

\(\alpha \)

\( \mu _1^{\prime }\)

\( \mu _2^{\prime }\)

\( \mu _3^{\prime }\)

\( \mu _4^{\prime }\)

\( \mu _5^{\prime }\)

SD

CV

CS

CK

0.98

1

0.6

0.57

0.0723

0.0481

0.0360

0.0288

0.0239

0.2071

2.8648

2.9628

10.7386

1

0.6

4.75

0.2054

0.1280

0.0927

0.0726

0.0596

0.2928

1.4254

1.2410

3.1952

1

1

0.57

0.0714

0.0481

0.0362

0.0290

0.0242

0.2073

2.9037

2.9873

10.8569

3

0.6

0.57

0.5220

0.3245

0.2341

0.1827

0.1497

0.2283

0.4373

0.8645

0.6740

3

0.6

4.75

0.0669

0.0419

0.0304

0.0237

0.0195

0.1935

2.8942

3.1116

11.9081

1.1

1

0.95

4.25

0.4592

0.3116

0.2354

0.1891

0.1580

0.3173

0.6910

−0.0034

1.7216

1

0.99

4.75

0.4849

0.3316

0.2516

0.2026

0.1695

0.3105

0.6404

−0.0906

1.7775

1

0.95

4.75

0.5108

0.3468

0.2622

0.2107

0.1760

0.2931

0.5739

−0.1089

1.8529

1

1

4.72

0.4750

0.3253

0.2470

0.1990

0.1666

0.3157

0.6647

−0.0689

1.7438

1

1

4

0.4775

0.3270

0.2484

0.2001

0.1675

0.3147

0.6590

−0.0761

1.7514

1.8

7

0.6

2.75

0.0728

0.0394

0.0264

0.0197

0.0157

0.1847

2.5370

2.9507

11.3585

7

0.6

0.57

0.0108

0.0056

0.0036

0.0027

0.0021

0.0738

6.8454

8.6215

85.3383

7

1

2.75

0.2558

0.1710

0.1280

0.1021

0.0848

0.3250

1.2703

0.8793

2.2813

7

1

0.57

0.0188

0.0105

0.0071

0.0054

0.0043

0.1007

5.3600

6.4319

47.3815

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