  We propose a new $L^2$-type goodness-of-fit test for the family of beta
distributions based on a conditional moment characterisation. The asymptotic
null distribution is identified, and since it depends on the underlying
parameters, a parametric bootstrap procedure is proposed. Consistency against
all alternatives that satisfy a convergence criterion is shown, and a Monte
Carlo simulation study indicates that the new procedure outperforms most of the
classical tests. Finally, the procedure is applied to a real data set related
to air humidity.
