Table 18 Parameter estimates and goodness-of fit statistics for data set VIII.

From: A new (T-X\(^\theta\)) family of distributions: properties, discretization and estimation with applications

Model

Estimates

-\(\varvec{\hat{ll}}\)

AIC

BIC

df

\(\varvec{\chi ^{2}}\)

p-value

DEE(\(\alpha , \theta , \beta\))

(0.025, 3.794, 1.6 \(\times 10^{-7}\))

268.8

543.59

550.29

5

8.078

0.152

DEW(\(\alpha , \theta , \beta , \eta\))

(0.723, 4.10, 5.7 \(\times 10^{-9}\), 0.69)

268.8

545.59

554.53

4

8.075

0.089

DEB(\(\alpha , \theta , \beta , \eta\))

( 2 \(\times 10^{-8}\), 4.42, 3.11, 0.071)

269.2

546.31

555.24

4

8.280

0.082

DEL(\(\alpha , \theta , \beta , \eta\))

(4.18, 3.79, 1.26, 7 \(\times 10^{-10}\))

268.8

545.59

554.53

4

8.076

0.089

DEFr(\(\alpha , \theta , \beta , \eta\))

(1.6 \(\times 10^{-8}\), 4.69, 0.011, 2.31)

268.8

545.64

554.58

4

8.023

0.091

DEG(\(\alpha , \theta , \beta , \eta\))

(5 \(\times\) e−09, 4.73, 1.36, 1.157)

268.8

545.61

554.55

4

8.035

0.090

DEETE(\(\alpha , \beta , \lambda\))

(43.64, 6.971, 0.012)

274.4

554.89

561.59

5

10.01

0.075

INH(\(\alpha , \beta\))

(3.363, 43.62)

286.2

576.43

580.90

6

24.36

0.0004

DEOWE(\(\alpha , \theta , \beta\))

(683.3, 0.128, 1.156)

268.3

542.63

549.34

5

5.910

0.315

PMiD(\(\alpha , \theta\))

(220.3, 0.059)

304.3

612.66

617.13

6

70.99

0

Geometric(p)

(0.019)

340.8

683.51

685.74

7

173.9

0