A.22 The probability that one beta variable is greater than another
Suppose π and ρ have independent beta distributions
Then
[see Altham (1969)]. For an expression (albeit a complicated one) for
see Weisberg (1972).
When α, β, γ and 
are large we can approximate the beta variables by normal variates of the same means and variances and hence approximate the distribution of 
by a normal distribution.
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