Table 1 Distribution of Corbet’s Malayan Buttery with zeros (Corbet 1942)

0

304

315.36

303.10

104.93

315.36

315.36

304.97

1

118

94.24

123.28

93.03

94.24

94.24

117.12

2

74

59.76

62.83

82.47

59.76

59.76

67.25

3

44

44.58

43.29

73.11

44.58

44.58

45.92

4

24

35.74

33.73

64.81

35.74

35.74

34.51

5

29

29.85

27.77

57.45

29.85

29.85

27.57

6

22

25.60

23.61

50.93

25.60

25.60

22.94

7

20

22.37

10.51

45.14

22.37

22.37

19.66

8

19

19.81

18.10

40.02

19.81

19.81

17.23

9

20

17.73

16.16

35.47

17.73

17.73

15.35

10

15

16.0

14.57

31.44

16.00

16.00

13.86

11

12

14.53

13.23

27.87

14.53

14.53

12.64

12

14

13.27

12.09

24.70

13.27

13.27

11.63

13

6

12.18

11.10

21.90

12.18

12.18

10.77

14

12

11.23

10.24

19.41

11.23

11.23

10.04

15

6

10.38

9.49

17.20

10.38

10.38

9.39

16

9

9.63

8.82

15.25

9.63

9.63

8.83

17

9

8.96

8.21

13.51

8.96

8.96

8.32

18

6

8.35

7.68

11.98

8.35

8.35

7.86

19

10

7.80

7.19

10.62

7.80

7.80

7.45

20

10

7.30

6.74

9.41

7.30

7.30

7.07

21

11

6.84

6.34

8.34

6.84

6.84

6.73

22

5

6.42

5.97

7.39

6.42

6.42

6.40

23

3

6.04

5.63

6.55

6.04

6.04

6.10

24

3

5.69

5.32

5.81

5.69

5.69

5.82

25+

119

114.36

119.00

45.27

114.36

114.36

118.57

Total

924

924

924

924

924

924

924

AIC

4516.22

4508.40

45021.16

4518.22

4518.22

4510.02

χ ²

28.50

19.46

660.91

28.50

28.50

18.57

p-value

0.20

0.62

0.00

0.15

0.15

0.61

MLEs

\( \widehat{\nu}=0.31 \)

\( \widehat{r}=0.26 \)

----

\( \widehat{\nu}=0.31 \)

\( \widehat{\nu}=0.31 \)

\( \widehat{\nu}=2.86 \)

\( \widehat{p}=0.97 \)

\( \widehat{p}=0.97 \)

\( \widehat{p}=0.01 \)

\( \widehat{p}=0.97 \)

\( \widehat{p}=0.97 \)

\( \widehat{p}=1.26 \)

\( \widehat{\lambda}=0.15 \)

\( \widehat{\alpha}=0.89 \)

\( \widehat{\alpha}=1.00 \)

---

\( \widehat{\alpha}=-1.07 \)

\( \widehat{\beta}=1.00 \)

\( \widehat{\beta}=-1.13 \)