Table 11 Goodness-of fit statistics for data set II.

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

Model

Estimates

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

AIC

BIC

AICc

K-S

p-value

E-X\(^{\theta }\)E\((\alpha , \theta )\)

(0.621, 0.928)

39.6

83.3

83.4

84.6

0.072

0.995

G-X\(^{\theta }\)L\((\alpha , \theta , \beta , c)\)

(1.84, 0.665, 0.45, 1.155)

39.96

87.9

88.3

85.9

0.077

0.988

G-X\(^{\theta }\)E\((\alpha , \theta , \beta )\)

(0.778, 1.33, 2.205)

39.6

85.2

85.5

84.9

0.078

0.986

Bu-X\(^{\theta }\)E\((\alpha , \theta , \beta )\)

(0.226, 1.004, 2.485)

39.87

85.7

86

85.6

0.083

0.975

CIR(\(\alpha , \beta\))

(0.718, 1.05)

40.68

85.4

85.8

88.2

0.078

0.985

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

(0.615, 4, 2.8)

39.89

85.7

86.8

89.9

0.080

0.983

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