Distribution

T

${\widehat{\alpha }}_0$

${\widehat{\alpha }}_1$

${\widehat{\beta }}_1$

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

Log likelihood

AIC

BIC

Normal

10

0.010567 (5.584000)

0.000000 (2.076000)

0.999999 (4.037000)

0.999999

−15.072110

−

−

50

0.030394 (0.113100)

0.000000 (NaN)

0.973356 (NaN)

0.973356

−72.035600

3.041424

3.194386

100

0.337239 (0.302450)

0.117460 (0.122990)

0.608080 (0.276460)+

0.725540

−151.425900

3.108517

3.212724

200

0.188907 (0.104230)−

0.203089 (0.091280)+

0.661254 (0.126880)+

0.864343

−303.794900

3.077949

3.143916

500

0.235710 (0.082880)+

0.328460 (0.074580)+

0.530400 (0.091810)+

0.858860

−775.677500

3.118710

3.152427

1000

0.250588 (0.065500)+

0.273907 (0.047630)+

0.570504 (0.068860)+

0.844411

−1566.367000

3.140734

3.160365

5000

0.186149 (0.019675)+

0.287085 (0.019708)+

0.615691 (0.022762)+

0.902776

−8045.231000

3.219692

3.224960

10,000

0.195478 (0.014640)+

0.292343 (0.014310)+

0.604074 (0.016860)+

0.896417

−16018.170000

3.204435

3.207319

Student-t

10

0.041899 (2.521000)

0.000000 (NaN)

1.000000 (2.483000)+

1.000000

−15.360760

−

−

50

0.048275 (0.136900)

0.000000 (NaN)

0.962590 (NaN)

0.962590

−72.806500

3.112260

3.303462

100

0.380179 (0.364950)

0.111464 (0.135180)

0.611736 (0.296710)+

0.723200

−152.889400

3.157788

3.288046

200

0.176107 (0.123220)

0.193886 (0.102850)−

0.699870 (0.142820)+

0.893756

−305.807400

3.108074

3.190532

500

0.241219 (0.095270)+

0.339037 (0.088100)+

0.546555 (0.100000)+

0.885592

−780.622900

3.142492

3.184638

1000

0.273102 (0.081940)+

0.287574 (0.058180)+

0.566611 (0.081620)+

0.854185

−1573.665000

3.157330

3.181869

5000

0.197582 (0.023408)+

0.303939 (0.023573)+

0.613669 (0.025556)+

0.917608

−8074.697000

3.231897

3.238396

10,000

0.205062 (0.017300)+

0.309223 (0.017050)+

0.604201 (0.018810)+

0.913424

−16078.450000

3.216689

3.220295

GED

10

1.103100 (0.771600)

0.000000 (NaN)

0.000000 (0.219800)

0.000000

−13.707760

−

−

50

0.047949 (0.090690)

0.000000 (NaN)

0.957198 (NaN)

0.957198−

71.303360

3.052134

3.243337

100

0.325748 (0.261280)

0.131951 (0.117220)

0.605605 (0.240930)+

0.737556

−150.586200

3.111725

3.241983

200

0.196608 (0.097550)+

0.212583 (0.089150)+

0.647040 (0.119580)+

0.859623

−303.439900

3.084399

3.166857

500

0.238595 (0.079250)+

0.332419 (0.070950)+

0.525230 (0.087600)+

0.857649

−774.979800

3.119919

3.162065

1000

0.248880 (0.063560)+

0.273870 (0.046440)+

0.571840 (0.066840)+

0.845710

−1566.181000

3.142361

3.166900

5000

0.186098 (0.019569)+

0.287009 (0.019601)+

0.615786 (0.022642)+

0.902795

−8045.173000

3.220069

3.226586

10,000

0.195530 (0.014520)+

0.292300 (0.014200)+

0.604070 (0.016730)+

0.896370

−16017.900000

3.204581

3.208186