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Table 1 Classical and Bayesian estimates of Shannon diversity index (SDI)

From: Diversity in substance use behaviour among street children of Delhi under Bayesian paradigm

S

p

n

\(\hat {H}(\boldsymbol {p})\)

   

\(\hat {H}^{B}(\boldsymbol {p})\)

   

\(V\left (\hat {H}(\boldsymbol {p})\right)\)

   

\(V\left (\hat {H}^{B}(\boldsymbol {p})\right)\)

   
   

S

   

S

   

S

   

S

   
   

1

2

3

4

1

2

3

4

1

2

3

4

1

2

3

4

2

(0.1,0.2)

10

1.37

1.53

  

1.86

1.86

  

1.16

1.19

  

0.040

0.030

  
 

(0.3,0.5)

10

1.76

1.88

  

1.78

1.94

  

1.17

1.05

  

0.046

0.014

  
 

(0.6,0.8)

10

1.96

1.90

  

2.01

2.02

  

0.96

1.01

  

0.007

0.007

  
 

(0.1,0.2)

50

1.82

1.90

  

1.77

1.94

  

1.06

0.84

  

0.040

0.010

  
 

(0.3,0.5)

50

1.96

1.97

  

2.04

2.02

  

0.69

0.57

  

0.003

0.002

  
 

(0.1,0.2)

100

1.93

1.95

  

2.05

1.99

  

0.81

0.63

  

0.008

0.003

  

3

(0.1,0.2)

10

1.73

2.09

0.76

 

2.54

2.67

2.45

 

1.14

1.18

0.74

 

0.147

0.011

0.160

 
 

(0.3,0.5)

10

2.46

2.54

2.55

 

2.75

2.82

2.85

 

1.02

1.02

0.97

 

0.007

0.001

0.050

 
 

(0.6,0.8)

10

2.55

2.54

2.57

 

2.60

2.69

2.65

 

0.85

0.90

0.83

 

0.021

0.051

0.024

 
 

(0.1,0.2)

50

2.52

2.54

2.57

 

2.74

2.68

2.69

 

0.82

0.81

0.75

 

0.010

0.023

0.022

 
 

(0.3,0.5)

50

2.56

2.57

2.58

 

2.75

2.65

2.74

 

0.51

0.52

0.47

 

0.004

0.013

0.007

 
 

(0.1,0.2)

100

2.55

2.56

2.58

 

2.60

2.65

2.76

 

0.59

0.59

0.53

 

0.018

0.013

0.009

 

4

(0.1,0.2)

10

2.63

2.88

2.88

2.16

3.33

3.66

3.45

3.37

1.12

1.14

1.10

1.20

0.039

0.030

0.048

0.039

 

(0.3,0.5)

10

2.88

2.76

2.80

2.92

2.95

3.21

3.37

3.13

0.85

0.99

1.03

0.95

0.023

0.058

0.073

0.082

 

(0.6,0.8)

10

2.96

2.96

2.95

2.96

3.00

2.90

3.02

2.94

0.73

0.75

0.78

0.76

0.045

0.006

0.062

0.074

 

(0.1,0.2)

50

2.91

2.87

2.87

2.93

2.91

3.00

3.31

3.15

0.63

0.79

0.84

0.75

0.006

0.109

0.099

0.093

 

(0.3,0.5)

50

2.98

2.97

2.97

2.98

2.91

3.02

3.27

2.90

0.39

0.48

0.51

0.45

0.006

0.062

0.101

0.006

 

(0.1,0.2)

100

2.96

2.96

2.97

2.97

2.83

2.91

3.02

2.91

0.55

0.52

0.53

0.47

0.000

0.006

0.062

0.006