Table 6 Partial and overall ranks ofBias, MSE, MRE for parameter estimatesunder different estimation methods.

From: A novel extension of the power lindley distribution with statistical properties and application to COVID-19 data

Sample

Size

Parameter

\(\kappa_{1}\)

\(\kappa_{2}\)

\(\kappa_{3}\)

\(\kappa_{4}\)

\(\kappa_{5}\)

\(\kappa_{6}\)

\(\kappa_{7}\)

\(\kappa_{8}\)

\(\kappa_{9}\)

\(\kappa_{10}\)

20

\(\alpha = 0.25\)

\(\beta = 0.05\)

\(\gamma = 0.50\)

\(\delta = 0.15\)

\(\lambda = 0.90\)

3

6

5

10

9

7

8

4

1

2

50

3

5

9.5

9.5

8

4

7

6

1

2

100

3

5.5

9

5.5

10

4

7

8

1

2

150

3

6

9

5

10

4

7

8

2

1

250

2

6

10

5

9

4

7

8

3

1

400

2

6

10

3

8

5

7

9

4

1

600

2

6

10

3

9

5

7

8

4

1

20

\(\alpha = 0.40\)

\(\beta = 0.10\)

\(\gamma = 0.35\)

\(\delta = 0.25\)

\(\lambda = 0.70\)

5

6

8.5

10

7

4

8.5

3

1

2

50

4

5

9

8

10

3

7

6

1

2

100

4

5

10

6

9

3

7

8

1

2

150

4

6

9

7

8

3

5

10

1

2

250

5

6

9

7

8

3

4

10

2

1

400

5

6

9

7

8

4

3

10

2

1

600

4

6

8

7

10

5

2

9

3

1

20

\(\alpha = 0.15\)

\(\beta = 1.05\)

\(\gamma = 1.30\)

\(\delta = 0.35\)

\(\lambda = 1.15\)

6

7

9.5

4

9.5

8

3

5

1

2

50

3

8

9

4

10

7

5

6

2

1

100

3

8

9

4

10

6

5

7

1

2

150

4

6

9

2

10

8

5

7

3

1

250

4

6

9

2

10

7

5

8

3

1

400

3

6

9

2

10

7

5

8

4

1

600

3

6

9

1

10

7

5

8

4

2

20

\(\alpha = 0.20\)

\(\beta = 0.95\)

\(\gamma = 1.15\)

\(\delta = 0.25\)

\(\lambda = 1.05\)

6

8

9

5

10

4

7

3

1

2

50

3

8

10

5

9

6

4

7

1

2

100

3

7

10

4

9

6

5

8

2

1

150

3

8

10

4

9

6

5

7

2

1

250

3

5

10

4

9

6

7

8

2

1

400

4

6

10

2

9

5

7

8

3

1

600

4

5.5

9

2

10

5.5

7

8

3

1

Sum all ranks

 

105

174

251.5

126

262.5

141.5

150.5

180

59

41

Over all ranks

 

[3]

[7]

[9]

[4]

[10]

[5]

[6]

[8]

[2]

[1]

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