Table 3 The number of books that were borrowed k times (Burrell and Cane 1982)

1

9647

9522.59

9557.15

9364.75

9604.38

9576.21

9648.57

2

4351

4595.67

4538.89

4706.62

4401.32

4458.54

4341.37

3

2275

2296.39

2296.51

2365.50

2314.68

2311.93

2291.26

4

1250

1167.09

1179.55

1188.87

1231.23

1213.94

1244.90

5

663

599.12

608.51

597.51

643.23

630.96

663.27

6

355

309.61

313.75

300.31

327.22

322.40

339.49

7

154

160.75

161.73

150.93

161.73

161.61

165.46

8

72

83.76

83.27

75.86

77.67

79.45

76.51

9

37

43.76

42.82

38.12

36.28

38.33

33.54

10

14

22.91

22.00

19.16

16.50

18.16

13.95

11

6

12.02

11.28

9.63

7.32

8.46

5.51

12

2

6.31

5.78

4.84

3.17

3.87

2.07

13

0

3.32

2.96

2.43

1.34

1.75

0.74

14

1

3.89

3.28

2.46

0.93

1.37

0.56

Total

18,827

18827.00

18827.00

18827.00

18827.00

18827.00

18827.00

AIC

52461.94

52453.14

52472.22

52414.70

52422.75

52411.67

χ ²

51.96

38.33

66.83

7.20

14.75

2.37

p-value

0.00

0.00

0.00

0.51

0.06

0.94

MLEs

\( \overset{\frown }{r}=0.81 \)

\( \overset{\frown }{v}=0.27 \)

\( \overset{\frown }{\theta }=0.00 \)

\( \overset{\frown }{v}=0.01 \)

\( \overset{\frown }{v}=0.01 \)

\( \overset{\frown }{v}=2.30 \)

\( \overset{\frown }{p}=0.53 \)

\( \overset{\frown }{p}=0.38 \)

\( \overset{\frown }{p}=0.50 \)

\( \overset{\frown }{p}=1.18 \)

\( \overset{\frown }{p}=0.93 \)

\( \overset{\frown }{p}=6.40 \)

\( \overset{\frown }{\beta }=1.78 \)

----

\( \overset{\frown }{\alpha }=1.37 \)

----

\( \overset{\frown }{\alpha }=-2.98 \)

\( \overset{\frown }{d}=1.16 \)

\( \overset{\frown }{\beta }=0.74 \)

\( \overset{\frown }{\beta }=-3.95 \)

\( \overset{\frown }{l}=1.03 \)