Table 2 The number of spots in southern pine beetle (Lin 1985)

0

1169

1165.32

1168.98

922.62

1168.56

1168.71

1169.00

1

144

169.40

148.01

373.44

152.87

151.88

147.59

2

92

78.91

82.91

151.15

80.17

80.69

84.21

3

54

45.18

51.87

61.18

49.76

50.13

52.00

4

29

28.28

33.51

24.76

32.60

32.75

33.17

5

18

18.61

21.93

10.02

21.80

21.82

21.54

6

10

12.65

14.44

4.06

14.68

14.64

14.14

7

12

8.78

9.55

1.64

9.89

9.84

9.36

8

6

6.20

6.32

0.66

6.65

6.60

6.23

9

9

4.44

4.19

0.27

4.45

4.41

4.16

10

3

3.20

2.78

0.11

2.96

2.93

2.79

11

2

2.33

1.85

0.04

1.96

1.94

1.88

12

0

1.71

1.23

0.02

1.29

1.28

1.27

13

0

1.26

0.81

0.01

0.84

0.84

0.85

14

1

0.93

0.54

0.00

0.55

0.55

0.58

15

0

0.69

0.36

0.00

0.35

0.35

0.39

16

0

0.52

0.24

0.00

0.23

0.23

0.27

17

0

0.39

0.16

0.00

0.15

0.15

0.18

18

0

0.29

0.11

0.00

0.09

0.09

0.12

19

1

0.92

0.22

0.00

0.15

0.16

0.28

Total

1550

1550.00

1550.00

1550.00

1550.00

1550.00

1550.00

AIC

3117.28

3116.33

3518.85

3113.24

3112.99

3113.84

χ ²

14.79

8.56

669.08

8.99

8.65

8.18

p-value

0.06

0.13

0.00

0.25

0.28

0.23

MLEs

\( \overset{\frown }{r}=0.18 \)

\( \overset{\frown }{v}=0.08 \)

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

\( \overset{\frown }{v}=0.13 \)

\( \overset{\frown }{v}=0.10 \)

\( \overset{\frown }{v}=0.002 \)

\( \overset{\frown }{p}=0.79 \)

\( \overset{\frown }{p}=0.59 \)

\( \overset{\frown }{p}=0.40 \)

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

\( \overset{\frown }{p}=0.98 \)

\( \overset{\frown }{p}=0.69 \)

\( \overset{\frown }{\beta }=2.03 \)

-----

\( \overset{\frown }{\alpha }=1.15 \)

----

\( \overset{\frown }{\alpha }=0.28 \)

\( \overset{\frown }{d}=0.68 \)

\( \overset{\frown }{\beta }=0.87 \)

\( \overset{\frown }{\beta }=0.28 \)

\( \overset{\frown }{l}=1.05 \)