Characterizations of Beta Probability Distributions Based on the Minimum χ2−Divergence Principle∗

The minimum χ2−divergence principle states:When a prior probability density function of X, g(x), which estimates the underlying probability density function f(x) is given in addition to some constraints, then among all the density functions f(x) which satisfy the given constraints we should select that proba-bility density function which minimizes the χ2−divergence. We study minimun χ2−divergence probability distributions based on this principle given a prior beta distribution and the partial information on moments