Some Researches On The Record Values Based On The Geometric Distribution

Record value is an important method of studying the varying trend of the random variables,and is a hot topic in theory and application of great significance in statistics in rencent years. The geometric distribution is an important discrete distribuion in the probability theory,and has been applied in more and more fields.Especially in IE, electrical engineering, control theory and economics, it plays a specially important role.Using the method of probability theory and combinatorial mathematics, the article studies the probabilistic nature of record values coming from the geometric distribution,including record values、weak record values、k th strong record values、 k th record values、kth weak record values.Firstly,by means of the index of record values joint distribution、conditional probability of record values and weak record vaules are given, and k th record values can be represented by the sum of independent random variables.Secondly,emphasize the distribution、joint distribution、 conditional probability of record value based on geometric distribution, and then prove the distributional properties of record values and weak record values and a character of k th record values、k th weak record values how to decide the geometric distribution.