Thus it is a bounded distribution that allows for outliers to have a greater chance of occurring than does the beta distribution.
22.
The Jeffreys interval is the Bayesian credible interval obtained when using the Jeffreys prior for this problem is a Beta distribution with parameters.
23.
Therefore, the harmonic mean ( " H X " ) of a beta distribution with shape parameters ? and ? is:
24.
The use of Beta distributions in Bayesian inference is due to the fact that they provide a family of Bernoulli ) and geometric distributions.
25.
This parametrization of the beta distribution may lead to a more intuitive understanding than the one based on the original parameters ? and ?.
26.
Equivalently, this result follows from the Cram�r Rao bound, since the Fisher information matrix components for the beta distribution are these logarithmic variances.
27.
Tajima ( 1989 ) found an empirical similarity between the distribution of the test statistic and a beta distribution with mean zero and variance one.
28.
Where " t " m is Student's t distribution, F is the F distribution and \ beta is the beta distribution.
29.
Higher order logarithmic moments can be derived by using the representation of a beta distribution as a proportion of two Gamma distributions and differentiating through the integral.
30.
The Beta function ( in the denominator of the beta distribution ) approaches infinity, for both parameters approaching zero, ?, ? ?! 0.
