Table 16 Parameter estimate and goodness-of fit statistics for data set VI.

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

(5.56, 1.1 \(\times\) e−9, 0.0011)

1187.28

2380.55

2390.26

10

14.35

0.158

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

( 0.121, 0.5, 0.062, 0.53)

1185.55

2379.09

2392.04

9

13.84

0.128

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

(0.206, 0.607, 0.041, 1.072)

1186.28

2380.57

2393.51

9

13.84

0.128

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

(0.273, 0.498, 0.22, 521.3)

1185.92

2379.84

2392.78

9

13.66

0.135

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

(0.60, 0.549, 0.024, 0.359)

1186.17

2380.33

2393.28

9

13.59

0.137

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

(0.015, 0.799, 6.29, 3.009)

1181.77

2371.54

2384.46

9

14.12

0.118

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

(0.72, 0.51, 0.007)

1191.46

2388.91

2398.62

10

18.54

0.047

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

(0.616,44.56)

1224.12

2452.25

2458.72

11

64.07

0

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

(0.204, 0.0017, 1.065)

1185.99

2377.98

2387.69

10

15.63

0.111

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

(0.005,0.0003)

1197.83

2399.67

2406.14

11

23.62

0.014

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

(2e−6, 5.3 \(\times\) e03)

1195.17

2394.34

2400.82

11

20.91

0.034

Geometric(p)

(0.0046)

1197.83

2397.67

2400.9

12

23.63

0.023