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Table 3 The MLEs of the parameters and SEs in parentheses and the goodness-of-fit statistics for D1

From: The odd log-logistic logarithmic generated family of distributions with applications in different areas

Model

μ

σ

α

β

\(\hat \ell _{n}\)

W

A

K-S

p-value

OLLLN

2.887

0.532

0.379

-1.639

126.178

0.035

0.331

0.053

0.963

 

(0.212)

(0.180)

(0.192)

(1.947)

     

Normal

2.557

1.112

  

128.119

0.092

0.608

0.092

0.445

 

(0.121)

(0.086)

       

EN

1.832

1.337

1.939

 

128.064

0.075

0.522

0.085

0.557

 

(2.366)

(0.708)

(3.878)

      

BN

0.808

2.443

7.113

2.469

128.085

0.074

0.520

0.084

0.562

 

(7.151)

(8.162)

(48.582)

(14.619)

     

GN

2.805

0.541

0.290

0.197

127.757

0.058

0.438

0.075

0.7105

 

(1.059)

(0.265)

(0.382)

(0.216)

     

KN

1.654

0.748

0.920

0.320

127.848

0.063

0.469

0.079

0.642

 

(1.067)

(0.539)

(1.017)

(0.524)

     

LN

3.172

1.079

 

-7.091

127.570

0.048

0.391

0.066

0.828

 

(0.562)

(0.094)

 

(16.134)

     

OLL-N

2.626

0.603

0.452

 

127.062

0.076

0.523

0.095

0.408

 

(0.126)

(0.218)

(0.232)