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Table 2 Moments and quantiles of the non-central bootstrap distributions

From: Testing the Rasch model with the conditional likelihood ratio test: sample size requirements and bootstrap algorithms

k/df

n

meth

mean

var

cv

skew

kurt

q50

q90

q95

q99

5/4

100

nv

4.46

9.80

0.70

1.39

2.90

3.75

8.65

10.54

14.70

  

free

4.65

10.07

0.68

1.31

2.64

4.01

8.89

10.73

14.82

  

fix

4.72

9.78

0.66

1.24

2.29

4.10

8.92

10.75

14.70

 

250

nv

50.60

123.32

0.22

0.25

0.02

50.14

65.15

69.58

78.32

  

free

14.89

27.97

0.36

0.75

0.86

14.19

21.97

24.66

30.01

  

fix

13.43

23.23

0.36

0.78

0.82

12.66

20.03

22.35

27.03

 

500

nv

5.07

12.34

0.69

1.34

2.63

4.30

9.81

11.83

16.42

  

free

4.65

10.64

0.70

1.38

2.87

3.91

9.01

10.95

15.29

  

fix

4.66

10.75

0.70

1.39

2.87

3.92

9.06

11.02

15.41

 

750

nv

9.36

29.00

0.58

0.98

1.32

8.45

16.61

19.47

25.63

  

free

6.77

18.59

0.64

1.16

1.89

5.93

12.61

15.03

20.20

  

fix

6.77

18.47

0.63

1.15

1.90

5.94

12.58

14.99

19.98

 

1000

nv

11.61

38.43

0.53

0.89

1.08

10.65

19.97

23.14

29.83

  

free

8.64

26.15

0.59

1.05

1.57

7.75

15.51

18.34

24.17

  

fix

8.80

26.28

0.58

1.03

1.50

7.93

15.66

18.47

24.53

 

2500

nv

9.82

31.20

0.57

1.00

1.46

8.91

17.33

20.24

26.67

  

free

6.95

19.47

0.63

1.14

1.83

6.10

12.91

15.39

20.71

  

fix

7.01

19.70

0.63

1.14

1.79

6.15

13.03

15.51

20.78

 

5000

nv

20.44

73.41

0.42

0.67

0.63

19.49

31.91

35.99

44.45

  

free

13.48

44.64

0.50

0.82

0.93

12.56

22.48

25.80

32.77

  

fix

13.95

45.78

0.48

0.79

0.88

13.06

23.05

26.33

33.54

10/9

100

nv

16.63

48.66

0.42

0.76

0.84

15.73

25.98

29.40

36.58

  

free

16.93

49.66

0.42

0.71

0.67

16.07

26.36

29.88

36.84

  

fix

17.76

53.02

0.41

0.70

0.66

16.90

27.50

31.02

38.17

 

250

nv

15.23

43.00

0.43

0.80

0.98

14.37

24.01

27.26

34.21

  

free

15.23

42.59

0.43

0.78

0.85

14.36

23.97

27.25

34.03

  

fix

15.83

45.04

0.42

0.77

0.83

14.97

24.82

28.11

35.05

 

500

nv

24.60

80.08

0.36

0.60

0.47

23.66

36.55

40.73

49.11

  

free

25.09

82.19

0.36

0.60

0.52

24.17

37.13

41.32

50.00

  

fix

26.38

88.22

0.36

0.61

0.52

25.42

38.92

43.31

52.47

 

750

nv

17.83

53.23

0.41

0.73

0.77

16.95

27.59

31.15

38.46

  

free

18.13

54.32

0.41

0.73

0.76

17.21

28.00

31.63

39.10

  

fix

18.83

57.38

0.40

0.72

0.77

17.90

28.96

32.67

40.32

 

1000

nv

19.13

58.74

0.40

0.71

0.71

18.22

29.33

33.11

40.76

  

free

20.03

62.19

0.39

0.69

0.67

19.13

30.53

34.31

42.26

  

fix

21.12

66.66

0.39

0.65

0.57

20.24

32.04

35.97

43.88

 

2500

nv

14.21

38.70

0.44

0.82

0.91

13.34

22.57

25.73

32.28

  

free

14.47

39.67

0.44

0.80

0.89

13.63

22.97

26.10

32.56

  

fix

14.96

42.22

0.43

0.80

0.93

14.11

23.64

26.98

33.72

 

5000

nv

15.19

42.61

0.43

0.79

0.90

14.31

23.92

27.23

33.92

  

free

15.14

42.54

0.43

0.80

0.92

14.27

23.86

27.15

33.93

  

fix

15.49

43.84

0.43

0.77

0.76

14.62

24.38

27.65

34.50

15/14

100

nv

21.08

56.32

0.36

0.68

0.66

20.23

31.10

34.73

42.13

  

free

21.59

58.86

0.36

0.66

0.61

20.74

31.86

35.45

42.99

  

fix

21.98

59.95

0.35

0.62

0.50

21.15

32.32

35.97

43.36

 

250

nv

27.02

80.26

0.33

0.60

0.52

26.13

38.94

43.13

51.73

  

free

28.16

84.17

0.33

0.57

0.44

27.30

40.38

44.68

53.11

  

fix

28.84

87.07

0.32

0.56

0.38

27.92

41.25

45.48

54.39

 

500

nv

20.85

55.05

0.36

0.66

0.62

20.05

30.72

34.36

41.78

  

free

20.85

55.55

0.36

0.67

0.64

20.01

30.76

34.34

41.62

  

fix

21.13

56.11

0.35

0.69

0.71

20.25

31.10

34.78

42.27

 

750

nv

27.01

80.95

0.33

0.60

0.51

26.08

39.02

43.18

51.58

  

free

27.86

82.61

0.33

0.59

0.60

27.01

39.87

44.06

52.72

  

fix

28.37

85.27

0.33

0.58

0.49

27.50

40.65

45.00

53.45

 

1000

nv

36.14

115.14

0.30

0.49

0.32

35.28

50.30

55.18

65.02

  

free

37.22

121.78

0.30

0.51

0.34

36.31

51.83

56.89

66.78

  

fix

38.39

124.94

0.29

0.49

0.35

37.49

53.20

58.22

68.15

 

2500

nv

24.07

68.46

0.34

0.62

0.54

23.20

35.08

38.98

47.12

  

free

24.78

71.02

0.34

0.62

0.55

23.90

36.02

39.95

48.09

  

fix

25.39

73.60

0.34

0.61

0.54

24.51

36.81

40.85

48.82

 

5000

nv

27.56

81.96

0.33

0.58

0.45

26.69

39.65

43.83

52.29

  

free

28.52

85.93

0.33

0.56

0.42

27.65

40.82

45.09

53.90

  

fix

29.17

89.11

0.32

0.58

0.47

28.26

41.71

46.07

55.00