Data set

Model

MLE

SD

$-2\log L$

AIC

BIC

K-S statistic

Critical value

Data 1

MQLD

$\widehat{\theta }=0.616$

0.056

208.235

214.235

218.537

0.131

$\widehat{\alpha }=0.013$

0.618

$\widehat{\delta }=18.934$

1.556

QLD

$\widehat{\theta }=3.25\times {10}^{-2}$

0.005

274.528

278.528

281.396

0.426

0.244

$\widehat{\alpha }=4.967\times {10}^3$

5.932

TwPLD

$\widehat{\theta }=0.032$

0.006

274.528

278.528

281.396

0.426

$\widehat{\alpha }=0.408$

5.931

LD

$\widehat{\theta }=0.063$

0.008

253.988

255.988

257.422

0.333

Data 2

MQLD

$\widehat{\theta }=0.926$

0.299

85.167

91.167

94.155

0.184

$\widehat{\alpha }=0.001$

2.970

$\widehat{\delta }=4.198$

1.274

QLD

$\widehat{\theta }=0.220$

0.004

100.473

104.473

106.465

0.278

0.304

$\widehat{\alpha }=3.982\times {10}^3$

5.932

TwPLD

$\widehat{\theta }=0.220$

0.049

100.473

104.473

106.465

0.278

$\widehat{\alpha }=0.167$

8.389

LD

$\widehat{\theta }=0.380$

0.061

94.065

96.065

97.061

0.211

Data 3

MQLD

$\widehat{\theta }=0.086$

0.021

300.5

306.5

312.236

0.076

$\widehat{\alpha }=0.094$

3.559