Table 17 Parameter estimates and goodness-of fit statistics for data set VII.

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

(8.98, 1.073, 3.3 \(\times 10^{-7}\))

263.12

532.34

537.33

3

1.469

0.689

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

(0.082, 1.84, 3.6 \(\times 10^{-5}\), 0.23)

263.17

534.34

540.99

2

1.469

0.479

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

(3 \(\times 10^{-6}\), 2.075, 2.017, 1.08)

263.17

534.34

540.99

2

1.475

0.478

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

(1.25, 1.07, 0.962, 2.4 \(\times 10^{-6}\))

263.18

534.35

541.00

2

1.484

0.476

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

(3 \(\times\) e−6, 2.07, 1.498, 0.015)

263.17

534.34

540.99

2

1.472

0.479

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

(0.01, 1.44, 0.63, 2.2 \(\times 10^{-6}\))

263.17

534.34

540.99

2

1.478

0.478

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

(2.57,1.207,0.003)

267.13

540.25

545.24

3

2.383

0.497

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

(1.037, 218.32)

281.98

567.97

571.29

4

17.65

0.001

DWMOE(\(\alpha , \theta , \beta\))

(0.005,1.0293)

266.79

537.59

540.91

4

2.86

0.582

DBiExII(\(\alpha , \theta\))

(0.005, 1.0293)

266.79

537.59

540.91

4

2.859

0.582

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

(0.0004, 0.0067)

264.96

533.92

537.35

4

1.592

0.810

Geometric(p)

(0.0024

273.93

549.86

551.52

5

13.01

0.023