Table 2 Relative efficiencies of ratio estimators for \({\lambda }_{2}\)=0.03.

From: Combination of memory type ratio and product estimators under extended EWMA statistic with application to wheat production

\(\lambda_{1}\)

\(0.1\)

\(0.15\)

\(0.25\)

\(0.5\)

\(0.75\)

\(1\)

Ρ

n

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)

0.05

10

18.44

24.84

11.87

14.04

6.95

7.53

2.92

2.98

1.63

1.64

0.98

0.98

20

18.81

25.21

12.05

14.23

6.94

7.51

2.93

2.98

1.63

1.63

0.98

0.98

30

18.06

24.08

12.17

14.33

6.76

7.30

2.95

3.01

1.64

1.65

0.98

0.98

50

18.78

25.21

11.91

14.06

6.87

7.44

2.92

2.98

1.63

1.64

0.98

0.98

200

17.90

23.86

12.20

14.44

6.89

7.46

2.96

3.02

1.64

1.64

0.98

0.98

500

18.69

25.15

11.78

13.89

6.82

7.38

2.94

3.00

1.63

1.64

0.98

0.98

0.25

10

19.88

26.52

13.04

15.37

7.42

8.02

3.19

3.26

1.77

1.77

1.06

1.06

20

20.75

27.63

12.93

15.22

7.43

8.04

3.17

3.24

1.77

1.78

1.07

1.07

30

20.42

27.28

12.78

15.10

7.35

7.94

3.19

3.25

1.77

1.78

1.06

1.06

50

19.92

26.63

13.14

15.50

7.42

8.02

3.20

3.26

1.76

1.77

1.06

1.06

200

20.91

28.10

13.34

15.79

7.53

8.15

3.19

3.26

1.77

1.78

1.06

1.06

500

20.78

27.95

13.40

15.84

7.51

8.14

3.19

3.25

1.78

1.79

1.06

1.06

0.50

10

23.00

30.66

14.91

17.67

8.38

9.08

3.55

3.62

1.98

1.99

1.18

1.18

20

23.01

30.97

14.46

17.08

8.26

8.94

3.59

3.66

1.99

1.99

1.19

1.19

30

22.17

29.52

14.57

17.22

8.32

9.01

3.58

3.66

1.98

1.99

1.19

1.19

50

22.67

30.27

14.58

17.21

8.37

9.06

3.58

3.65

1.99

2.00

1.19

1.19

200

22.60

30.03

14.94

17.66

8.40

9.08

3.56

3.63

1.99

2.00

1.19

1.19

500

22.83

30.65

15.00

17.76

8.34

9.02

3.59

3.66

1.98

1.99

1.19

1.19

0.75

10

24.81

33.09

16.93

20.09

9.60

10.40

4.06

4.15

2.24

2.25

1.34

1.34

20

24.86

33.04

16.39

19.32

9.41

10.19

4.05

4.13

2.25

2.26

1.35

1.35

30

25.41

33.82

16.37

19.36

9.47

10.24

4.06

4.14

2.24

2.25

1.35

1.35

50

26.32

35.16

16.83

19.90

9.60

10.39

4.04

4.12

2.26

2.26

1.35

1.35

200

26.26

35.11

16.87

19.99

9.55

10.33

4.08

4.16

2.26

2.27

1.35

1.35

500

25.37

34.18

16.41

19.35

9.55

10.34

4.05

4.13

2.24

2.25

1.35

1.35

0.95

10

29.52

39.78

18.81

22.26

10.59

11.47

4.54

4.63

2.52

2.53

1.50

1.50

20

29.23

39.04

18.30

21.64

10.68

11.55

4.57

4.66

2.52

2.53

1.51

1.51

30

28.55

38.23

18.72

22.07

10.46

11.32

4.56

4.65

2.52

2.53

1.51

1.51

50

28.81

38.45

18.58

21.91

10.63

11.49

4.54

4.63

2.52

2.53

1.51

1.51

200

27.91

36.84

18.67

22.04

10.67

11.53

4.54

4.63

2.52

2.53

1.51

1.51

500

27.28

36.19

18.10

21.37

10.58

11.45

4.54

4.63

2.53

2.54

1.51

1.51

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