Table 15 Parameter estimate and goodness-of fit statistics data set V.

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

(0.0382, 0.658, 0.0107)

277.25

561.44

566.79

3

0.989

0.804

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

(0.0467, 0.623, 0.002, 1.345)

277.25

562.49

569.64

2

1.037

0.595

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

(0.102, 0.764, 0.012, 2.733)

280.93

569.86

576.99

2

4.003

0.135

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

(0.0428, 0.641, 80.58, 0.0001)

277.74

563.47

570.61

2

0.981

0.613

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

(0.299, 0.3999, 0.642, 140.49)

277.31

562.61

569.75

2

1.298

0.523

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

(0.047, 0.622, 1.585, 0.0175)

277.25

562.50

569.64

2

1.099

0.577

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

(1.078, 1.1685, 0.0040)

282.03

570.06

575.41

3

4.506

0.212

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

(1.0229, 76.911),

279.46

562.92

566.49

4

2.268

0.687

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

(334.34, 0.0415, 0.380)

282.04

570.08

575.43

3

3.47

0.324

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

(0.0044, 0.00085)

282.09

568.19

571.76

4

4.739

0.315

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

(1.7 \(\times 10^{-6}\), 0.005)

281.68

567.37

570.93

4

4.497

0.343

Geometric(p)

(0.0044)

282.09

566.19

567.97

5

4.741

0.448