Distribution

T

${\widehat{\alpha }}_0$

${\widehat{\alpha }}_1$

${\widehat{\beta }}_1$

${\widehat{\alpha }}_1+{\widehat{\beta }}_1$

Log likelihood

AIC

BIC

Normal

10

0.000000 (0.570200)

0.000000 (0.262300)

0.957920 (0.088500)

0.957920

−10.105930

−

−

50

0.355595 (0.212110)−

0.908470 (0.567220)

0.099880 (0.233830)

1.008350

−75.350940

3.174037

3.326999

100

0.176660 (0.112450)

0.591960 (0.198480)+

0.433380 (0.114230)+

1.025340

−174.131300

3.562626

3.666833

200

0.132731 (0.056190)+

0.726780 (0.168860)+

0.379410 (0.082660)+

1.106190

−325.710400

3.297104

3.363071

500

0.199371 (0.048990)+

0.541618 (0.084920)+

0.430570 (0.061050)+

0.972188

−814.478900

3.273916

3.307632

1000

0.234100 (0.039710)+

0.571080 (0.059930)+

0.390790 (0.041180)+

0.961870

−1622.476000

3.252952

3.272583

5000

0.282421 (0.021652)+

0.512348 (0.026020)+

0.404431 (0.020987)+

0.916779

−8301.752000

3.322301

3.327515

10,000

0.291385 (0.016129)+

0.503095 (0.018866)+

0.399800 (0.015961)+

0.902895

−16403.060000

3.281411

3.284296

Student-t

10

0.356143 (0.746200)

0.000000 (NaN)

0.274409 (1.342000)

0.274409

−10.320510

−

−

50

0.371950 (0.268300)

0.636810 (0.534800)

0.230110 (0.315900)

0.866920

−75.505420

3.174037

3.326999

100

0.211810 (0.141300)

0.598000 (0.225400)+

0.439980 (0.124700)+

1.037980

−175.200000

3.604000

3.734259

200

0.154351 (0.071310)+

0.691809 (0.190020)+

0.400210 (0.093180)+

1.092019

−326.825000

3.318250

3.400708

500

0.211163 (0.057500)+

0.566390 (0.100150)+

0.429000 (0.066460)+

0.995390

−816.651100

3.286604

3.328750

1000

0.251439 (0.047340)+

0.595540 (0.071070)+

0.390030 (0.045710)+

0.985570

−1628.511000

3.267022

3.291561

5000

0.293727 (0.025399)+

0.546251 (0.031364)+

0.406134 (0.023220)+

0.952385

−8338.962000

3.337585

3.344102

10,000

0.303475 (0.018956)+

0.530203 (0.022519)+

0.403371 (0.017714)+

0.933574

−16468.990000

3.294799

3.298404

GED

10

0.000000 (0.216600)

0.000000 (0.276800)

0.938830 (NaN)

0.938830

−9.027367

−

−

50

0.351430 (0.199280)−

0.967760 (0.661110)

0.081150 (0.211370)

1.048910

−75.340620

3.213625

3.404827

100

0.165450 (0.100870)

0.616560 (0.194820)+

0.426530 (0.106840)+

1.043090

−173.848800

3.576977

3.707235

200

0.133698 (0.057600)+

0.721260 (0.173890)+

0.381240 (0.084590)+

1.102500

−325.699500

3.306995

3.389453

500

0.199755 (0.049660)+

0.541780 (0.086040)+

0.430187 (0.061760)+

0.971967

−814.441100

3.277764

3.319910

1000

0.234410 (0.040060)+

0.570870 (0.060380)+

0.390680 (0.041490)+

0.961550

−1622.454000

3.254907

3.279446

5000

0.283039 (0.021223)+

0.511903 (0.025430)+

0.404275 (0.020548)+

0.916178

−8300.768000

3.322307

3.328824

10,000

0.291607 (0.015976)+

0.503143 (0.018674)+

0.399615 (0.015806)+

0.902758

−16402.630000

3.281526

3.285131