Table 2 Shape parameters [ a,b] of beta distribution given mode m and variance τ ²

0.01

[1.33,33.99]

[1.12,12.73]

[1.07,8.18]

[1.05,6.21]

[1.04,5.05]

[1.03,4.26]

[1.03,3.67]

[1.02,3.21]

[1.02,2.84]

[1.02,2.53]

[1.01,2.26]

[1.01,2.03]

[1.01,1.82]

[1.01,1.63]

[1.01,1.45]

[1,1.28]

[1,1.12]

0.05

[3.89,55.92]

[1.77,15.55]

[1.43,9.21]

[1.3,6.74]

[1.23,5.36]

[1.18,4.45]

[1.15,3.79]

[1.12,3.29]

[1.1,2.89]

[1.08,2.56]

[1.07,2.28]

[1.05,2.03]

[1.04,1.82]

[1.03,1.62]

[1.02,1.44]

[1.02,1.28]

[1.01,1.11]

0.1

[10.36,85.26]

[3.05,19.4]

[2.07,10.59]

[1.72,7.44]

[1.53,5.76]

[1.41,4.7]

[1.33,3.95]

[1.27,3.39]

[1.22,2.95]

[1.18,2.59]

[1.14,2.3]

[1.12,2.04]

[1.09,1.82]

[1.07,1.62]

[1.05,1.44]

[1.03,1.27]

[1.01,1.11]

0.15

[20.24,110]

[4.88,23.01]

[2.93,11.91]

[2.25,8.1]

[1.91,6.14]

[1.69,4.92]

[1.55,4.09]

[1.44,3.48]

[1.35,3]

[1.29,2.62]

[1.23,2.31]

[1.18,2.04]

[1.14,1.81]

[1.11,1.61]

[1.08,1.43]

[1.05,1.26]

[1.02,1.1]

0.2

[32.84,128.38]

[7.22,25.89]

[4,13]

[2.91,8.65]

[2.36,6.45]

[2.03,5.11]

[1.8,4.2]

[1.64,3.54]

[1.51,3.04]

[1.41,2.64]

[1.33,2.31]

[1.26,2.04]

[1.2,1.8]

[1.15,1.6]

[1.1,1.41]

[1.06,1.25]

[1.02,1.1]

0.25

[47.46,140.37]

[9.95,27.84]

[5.25,13.75]

[3.68,9.03]

[2.89,6.66]

[2.41,5.23]

[2.09,4.27]

[1.86,3.57]

[1.68,3.05]

[1.55,2.63]

[1.43,2.3]

[1.34,2.02]

[1.26,1.78]

[1.19,1.58]

[1.13,1.4]

[1.08,1.24]

[1.03,1.09]

0.3

[63.33,146.43]

[12.92,28.82]

[6.62,14.11]

[4.52,9.21]

[3.46,6.75]

[2.83,5.27]

[2.4,4.28]

[2.1,3.57]

[1.87,3.03]

[1.69,2.61]

[1.55,2.27]

[1.43,1.99]

[1.33,1.76]

[1.24,1.56]

[1.16,1.38]

[1.1,1.23]

[1.04,1.09]

0.35

[79.71,147.18]

[16.01,28.88]

[8.05,14.09]

[5.39,9.16]

[4.06,6.69]

[3.27,5.21]

[2.73,4.22]

[2.35,3.51]

[2.07,2.98]

[1.84,2.56]

[1.66,2.23]

[1.52,1.96]

[1.39,1.73]

[1.29,1.53]

[1.2,1.36]

[1.12,1.21]

[1.04,1.08]

0.4

[95.87,143.3]

[19.07,28.1]

[9.47,13.7]

[6.27,8.9]

[4.67,6.5]

[3.71,5.06]

[3.06,4.1]

[2.61,3.41]

[2.26,2.89]

[2,2.49]

[1.78,2.17]

[1.61,1.91]

[1.46,1.69]

[1.33,1.5]

[1.23,1.34]

[1.13,1.2]

[1.05,1.08]

0.45

[111.04,135.5]

[21.94,26.6]

[10.81,12.99]

[7.09,8.45]

[5.24,6.18]

[4.12,4.82]

[3.38,3.91]

[2.85,3.26]

[2.45,2.77]

[2.14,2.4]

[1.89,2.09]

[1.69,1.85]

[1.52,1.64]

[1.38,1.46]

[1.26,1.31]

[1.15,1.18]

[1.06,1.07]

0.5

[124.5,124.5]

[24.5,24.5]

[12,12]

[7.83,7.83]

[5.75,5.75]

[4.5,4.5]

[3.67,3.67]

[3.07,3.07]

[2.63,2.63]

[2.28,2.28]

[2,2]

[1.77,1.77]

[1.58,1.58]

[1.42,1.42]

[1.29,1.29]

[1.17,1.17]

[1.06,1.06]

0.55

[135.5,111.04]

[26.6,21.94]

[12.99,10.81]

[8.45,7.09]

[6.18,5.24]

[4.82,4.12]

[3.91,3.38]

[3.26,2.85]

[2.77,2.45]

[2.4,2.14]

[2.09,1.89]

[1.85,1.69]

[1.64,1.52]

[1.46,1.38]

[1.31,1.26]

[1.18,1.15]

[1.07,1.06]

0.6

[143.3,95.87]

[28.1,19.07]

[13.7,9.47]

[8.9,6.27]

[6.5,4.67]

[5.06,3.71]

[4.1,3.06]

[3.41,2.61]

[2.89,2.26]

[2.49,2]

[2.17,1.78]

[1.91,1.61]

[1.69,1.46]

[1.5,1.33]

[1.34,1.23]

[1.2,1.13]

[1.08,1.05]

0.65

[147.18,79.71]

[28.88,16.01]

[14.09,8.05]

[9.16,5.39]

[6.69,4.06]

[5.21,3.27]

[4.22,2.73]

[3.51,2.35]

[2.98,2.07]

[2.56,1.84]

[2.23,1.66]

[1.96,1.52]

[1.73,1.39]

[1.53,1.29]

[1.36,1.2]

[1.21,1.12]

[1.08,1.04]

0.7

[146.43,63.33]

[28.82,12.92]

[14.11,6.62]

[9.21,4.52]

[6.75,3.46]

[5.27,2.83]

[4.28,2.4]

[3.57,2.1]

[3.03,1.87]

[2.61,1.69]

[2.27,1.55]

[1.99,1.43]

[1.76,1.33]

[1.56,1.24]

[1.38,1.16]

[1.23,1.1]

[1.09,1.04]

0.75

[140.37,47.46]

[27.84,9.95]

[13.75,5.25]

[9.03,3.68]

[6.66,2.89]

[5.23,2.41]

[4.27,2.09]

[3.57,1.86]

[3.05,1.68]

[2.63,1.55]

[2.3,1.43]

[2.02,1.34]

[1.78,1.26]

[1.58,1.19]

[1.4,1.13]

[1.24,1.08]

[1.09,1.03]

0.8

[128.38,32.84]

[25.89,7.22]

[13,4]

[8.65,2.91]

[6.45,2.36]

[5.11,2.03]

[4.2,1.8]

[3.54,1.64]

[3.04,1.51]

[2.64,1.41]

[2.31,1.33]

[2.04,1.26]

[1.8,1.2]

[1.6,1.15]

[1.41,1.1]

[1.25,1.06]

[1.1,1.02]

0.85

[110,20.24]

[23.01,4.88]

[11.91,2.93]

[8.1,2.25]

[6.14,1.91]

[4.92,1.69]

[4.09,1.55]

[3.48,1.44]

[3,1.35]

[2.62,1.29]

[2.31,1.23]

[2.04,1.18]

[1.81,1.14]

[1.61,1.11]

[1.43,1.08]

[1.26,1.05]

[1.1,1.02]

0.9

[85.26,10.36]

[19.4,3.05]

[10.59,2.07]

[7.44,1.72]

[5.76,1.53]

[4.7,1.41]

[3.95,1.33]

[3.39,1.27]

[2.95,1.22]

[2.59,1.18]

[2.3,1.14]

[2.04,1.12]

[1.82,1.09]

[1.62,1.07]

[1.44,1.05]

[1.27,1.03]

[1.11,1.01]

0.95

[55.93,3.89]

[15.55,1.77]

[9.21,1.43]

[6.74,1.3]

[5.36,1.23]

[4.45,1.18]

[3.79,1.15]

[3.29,1.12]

[2.89,1.1]

[2.56,1.08]

[2.28,1.07]

[2.03,1.05]

[1.82,1.04]

[1.62,1.03]

[1.44,1.02]

[1.28,1.02]

[1.11,1.01]

0.99

[33.99,1.33]

[12.73,1.12]

[8.18,1.07]

[6.21,1.05]

[5.05,1.04]

[4.26,1.03]

[3.67,1.03]

[3.21,1.02]

[2.84,1.02]

[2.53,1.02]

[2.26,1.01]

[2.03,1.01]

[1.82,1.01]

[1.63,1.01]

[1.45,1.01]

[1.28,1.003]

[1.12,1.001]