Distribution

T

${\widehat{\alpha }}_0$

${\widehat{\alpha }}_1$

${\widehat{\beta }}_1$

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

Log likelihood

AIC

BIC

Normal

10

0.092797 (0.312300)

0.000000 (NaN)

0.792543 (0.509600)

0.792543

−10.387690

−

−

50

0.247205 (NaN)

0.000000 (NaN)

0.683000 (NaN)

0.683000

−64.543000

2.741720

2.894682

100

0.515391 (0.243710)+

0.313620 (0.171160)−

0.218490 (0.250100)

0.532110

−142.382500

2.927651

3.031857

200

0.551310 (0.276030)+

0.241840 (0.115070)+

0.219900 (0.296190)

0.461740

−281.256800

2.852568

2.918535

500

0.280581 (0.128830)+

0.192765 (0.070340)+

0.478952 (0.183970)+

0.671717

−658.115800

2.648463

2.682180

1000

0.266805 (0.125850)+

0.175380 (0.053660)+

0.490860 (0.192250)+

0.666240

−1287.413000

2.582825

2.602456

5000

0.076052 (0.015230)+

0.079810 (0.010950)+

0.838810 (0.023180)+

0.918620

−6835.653000

2.735861

2.741075

10,000

0.084648 (0.011625)+

0.083991 (0.007755)+

0.830173 (0.016455)+

0.914164

−13925.400000

2.785880

2.788764

Student-t

10

0.498260 (NaN)

0.000000 (0.298900)

0.000000 (NaN)

0.000000

−10.492690

−

−

50

0.672763 (0.508600)

0.219563 (0.363600)

0.000000 (8.069000)

0.219563

−64.720050

2.788802

2.980004

100

0.553297 (0.274740)+

0.353272 (0.202200)−

0.202750 (0.256300)

0.556022

−143.339700

2.966794

3.097052

200

0.597735 (0.333200)−

0.265164 (0.135430)−

0.209946 (0.332220)

0.475110

−283.492100

2.884921

2.967379

500

0.289317 (0.155560)−

0.197990 (0.080630)+

0.500066 (0.206780)+

0.698056

−663.669500

2.674678

2.716824

1000

0.257727 (0.141860)−

0.176616 (0.061980)+

0.534789 (0.204610)+

0.711405

−1298.200000

2.606400

2.630939

5000

0.081890 (0.018530)+

0.084449 (0.013050)+

0.836469 (0.026660)+

0.920918

−6862.990000

2.747196

2.753713

10,000

0.096489 (0.014543)+

0.088165 (0.009244)+

0.822432 (0.019272)+

0.910597

−13972.050000

2.795410

2.799015

GED

10

0.310868 (0.802300)

0.000000 (NaN)

0.345600 (1.489000)

0.345600

−10.384230

−

−

50

0.259707 (NaN)

0.000000 (NaN)

0.667073 (NaN)

0.667073

−64.520510

2.780820

2.972023

100

0.514520 (0.238940)+

0.309120 (0.166260)−

0.222655 (0.247130)

0.531775

−142.341600

2.946832

3.077091

200

0.547422 (0.256370)+

0.239650 (0.108330)+

0.226142 (0.275200)

0.465792

−280.949600

2.859496

2.941954

500

0.284677 (0.116350)+

0.197720 (0.066270)+

0.469630 (0.166230)+

0.667350

−656.621700

2.646487

2.688633

1000

0.277384 (0.116370)+

0.180498 (0.050030)+

0.472655 (0.176830)+

0.653153

−1284.796000

2.579592

2.604131

5000

0.076030 (0.015200)+

0.079815 (0.010920)+

0.838836 (0.023130)+

0.918651

−6835.645000

2.736258

2.742775

10,000

0.084918 (0.011736)+

0.083987 (0.007809)+

0.829889 (0.016596)+

0.913876

−13925.210000

2.786042

2.789647