Based On Constrained Choice Probability Density Function Of The Maximum Entropy Method To Estimate

Probability density function contains almost all of the random variable information,according to have the sample data to estimate the probability density function of random variables,the probability density function is estimated,it is a basic problem in probability and mathematical statistics.At the same time,in many practical problems related application study,and on this basis,to develop this knowledge and problems in the field of research and discussion.The probability density function is estimated in the theoretical research and practical engineering application plays a very important role.According to the traditional method to estimate the probability density function of classification standard,the research of this problem can be divided into the following three categories:the parameterized method,the ginseng and half way.Because in most application study,associated with the real problems for the probability density function of the specific model of information often don't know,so,like this kind of problem solving is usually not assembly using parameterized method and a half.Based on this consideration,makes the reference method people in the study of probability density function estimation problem when the most popular a kind of method.In the method,because the nuclear method will eventually show to the probability density function of the specific solution,thus research and used widely.In spite of this,to estimate the probability density function using kernel method,there is still a kernel function and window width is difficult to determine the fault.Based on this,this article in the case of a deep understanding of the maximum entropy principle,aiming at how to common distribution parameter estimation were described in detail,and summarized the common distribution based on the principle of the maximum entropy to carry out the general steps of parameter estimation.The idea of the maximum entropy principle is roughly as follows:some constraints in a given situation,out of accord with the distribution of these constraints,choose the distribution of the maximum entropy as the ideal distribution is reasonable.And in view of the practical problems,to make the distribution of the derived from to study consistent with the known information system,find out to determine the distribution of constraints became using maximum entropy principle to estimate the probability density function of the key.Is based on such consideration,this paper puts forward a effective way to select constraints,on the basis of using the maximum entropy principle to estimate the probability density function.Simulation data show that the method can be reasonably selected data under the real distributed based on the maximum entropy principle to satisfy the constraints,and draw the conclusion:based on the method in this paper,the choice of constraint using the maximum entropy principle to estimate the probability density function is indeed a both from theory and for implementation is easy and effective method.