Table 3 Estimation results for times of failure data.

From: A novel Compound-Pareto model with applications and reliability peaks above a random threshold value at risk analysis

Model

Estimates

CPII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2},\mathbf {\xi }_{3}\right)\)

8.6\(\times\)10\(^{3}\)

3.88956

3.86\(\times\)10\(^{-2}\)

  

(6.9\(\times\)10\(^{1}\))

(0.03840)

(1.21\(\times\)10\(^{-2}\))

  

McPII\(\left( a,b,\mathbf {\xi }_{1},\mathbf {\xi }_{2}, \mathbf {\xi }_{3}\right)\)

2.187521

119.1751

12.41714

19.92433

75.6606

(0.5211)

(140.297)

(20.845)

(38.9601)

(147.24)

TTLPII\(\left( a,\mathbf {\xi }_{1},\mathbf {\xi }_{2},\mathbf {\xi }_{3}\right)\)

−0.80751

2.47663

(15608.2)

(38628.3)

 

(0.13962)

(0.54176)

(1602.37)

(123.936)

 

KmPII\(\left( a,\mathbf {\xi }_{1},\mathbf {\xi }_{2}, \mathbf {\xi }_{3}\right)\)

2.6150

100.2756

5.27710

78.6774

 

(0.3822)

(120.486)

(9.8116)

(186.005)

 

BPII\(\left( a,\mathbf {\xi }_{1},\mathbf {\xi }_{2},\mathbf {\xi }_{3}\right)\)

3.60360

33.63870

4.830700

118.8374

 

(0.6187)

(63.7145)

(9.23820)

(428.927)

 

PRHRPII\(\left( \mathbf {\xi }_{2},\mathbf {\xi }_{1},\mathbf {\xi }_{2}\right)\)

3.73\(\times\)10\(^{6}\)

4.707\(\times\)10\(^{-1}\)

4.49\(\times\)10\(^{6}\)

  

(1.01\(\times\)10\(^{6}\))

(0.00051)

(37.14684)

  

RTTLPII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2},\mathbf {\xi }_{1}\right)\)

−0.84732

5.52057

1.15678

  

(0.10010)

(1.18479)

(0.09588)

  

SGMPII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2},\mathbf {\xi }_{3}\right)\)

−1.04\(\times\)10\(^{-1}\)

9.83\(\times\)10\(^{6}\)

1.18\(\times\)10\(^{7}\)

  

(0.1223)

(4843.3)

(501.04)

  

OLLPII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2},\mathbf {\xi }_{3}\right)\)

2.32636

(7.17\(\times\)10\(^{5}\))

2.34\(\times\)10\(^{6}\))

  

(2.14\(\times\)10\(^{-1}\))

(1.19\(\times\)10\(^{4}\))

(2.61\(\times\)10\(^{1}\))

  

GaPII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2},\mathbf {\xi }_{3}\right)\)

3.58760

52001.49

37029.66

  

(0.5133)

(7955.00)

(81.1644)

  

EPII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2},\mathbf {\xi }_{3}\right)\)

3.62610

20074.51

26257.68

  

(0.6236)

(2041.83)

(99.7417)

  

ROLLPII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2}\right)\)

3.890564

0.573161

   

(0.36524)

(0.01946)

   

RBHPII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2}\right)\)

10801754

51367189

   

(983309)

(232312)

   

PII\(\left( \mathbf {\xi }_{1},\mathbf {\xi }_{2}\right)\)

51425.35

131789.8

   

(5933.49)

(296.119)

   
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