Editing Beta distribution (section)

====Mean, geometric mean and harmonic mean relationship====
[[File:Mean, Median, Geometric Mean and Harmonic Mean for Beta distribution with alpha = beta from 0 to 5 - J. Rodal.png|thumb|:Mean, median, geometric mean and harmonic mean for beta distribution with 0 < ''α'' = ''β'' < 5]]

It is known from the [[inequality of arithmetic and geometric means]] that the geometric mean is lower than the mean.  Similarly, the harmonic mean is lower than the geometric mean.  The accompanying plot shows that for ''α'' = ''β'', both the mean and the median are exactly equal to 1/2, regardless of the value of ''α'' = ''β'', and the mode is also equal to 1/2 for ''α'' = ''β'' > 1, however the geometric and harmonic means are lower than 1/2 and they only approach this value asymptotically as ''α'' = ''β'' → ∞.