可测函数的K-L信息最小化

The Minimization of K-L Information for Measurable Function

将K-L信息D(p,p0)推广到p0为非负有限可测函数,讨论了D(p,p0)在定义域约束、可测函数组的期望值约束和同时具有两个约束条件下的最小化问题,以及它们的逆问题.指出任何均匀分布族、负指数分布族和正则指数分布族都是最小化广义K-L信息的解.

K-L information D（p,p0 ） is extended to non negative measurable function under domain constraint or expectation constraints or both, and the inverse problem is discussed. It is pointed out that the uniform distribution, negative exponential distribution and regular exponential type distribution are the solution of this problem.