A Number Of Discrete Distribution Characteristics

This artical is composed of two parts which are the moments fornon-negative integer random variables and several conclusions for theapproach property of geometric distribution as well. We present asufficient and necessary condition of geometric distribution for therandom variables on the dNBUE class（discrete new better than used inexpectation class of life distribution） and dHNBUE class （discreteharmonic new better than used in expectation class of life distribution）.Furthermore, we give the corresponding promotion for severalconclusions about the approach property of geometric distribution.This article gives the key results with respect to the following threeaspects:1. The moments for non-negative integer random variables.（1）Weobtain a method for getting a variety of moments of the poissondistribution, binomial distribution, geometric distribution and negativebinomial distribution.（2）For two kinds of geometric distribution,therelationship between their moments are discussed.2. Several conclusions for the approach property of geometricdistribution:（1）We carry out the research on several typical numericalcharacteristics of geometric distribution and give the correspondingpromotion and proof for several conclusions. Meanwhile, We present asufficient and necessary condition of geometric distribution for therandom variables on the dNBUE and dHNBUE class of life distributions.（2）Make a study of the dNBUE class of life distribution and theapproach property of geometric distribution.（3）Several conclusions forthe dHNBUE class of life distribution are proposed.3. Several conclusions for the moments of non-negative integerrandom variables.The relationship to a variety of moments fornon-negative integer random variables is studied in this part.