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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