A.10 Beta distribution

X has a beta distribution with parameters α and β, denoted

if it has density

where the beta function is defined by

The mean and variance are

The mode is

and the approximate relationship between mean, mode and median can be used to find an approximate median.

The distribution function of any variable with a beta distribution is easily found in terms of the incomplete beta function

Extensive tables can be found in Pearson (1968) or in Pearson and Hartley (1966, Table 17).