A Class Of Reliable Weighted Exponential Distribution

Exponential distribution is a family of basic probability distribution inprobability theory and statistics. In mathematical statistics, the exponentialdistribution has an extremely important position and research significance. Thus, theresearch work of exponential distributions has been enduring and the research contenthas its own characteristics.The exponential distribution has attracted the researchers’ attention because itsummarizes the common features of a large class of distribution families and haspractical applied value. Simultaneously, only can the index structure completely solvemany important problems in theory. To better lay theoretical foundation for theresearch of other fields, we will continuously explore new exponential distributionsand give full play to the practical application of exponential distributions. Moreover,the applied research in system reliability stays in the stage of exponential distributionwith single parameter. This paper hopes to apply two-parameter exponentialdistribution to the research of system reliability.In this paper, we introduce a new double parameters exponential model and giveit some statistical significance. Making this new double parameters weighted indexdistribution as the main line, we will study its some properties. Further, we will studythe estimations of unknown parameters and consider the resulting estimation whethersatisfy the asymptotic normality. Final, expand it to the research of new Lomaxdistribution.Chapter one, we mainly introduced the research status of exponentialdistributions and the missing data. Then, we give the premise of the study and somerelevant knowledge.Chapter two, we first present a new class of weighted exponential distributionmodel, then study its basic properties and special properties, and make its maximumlikelihood estimation of unknown parameters. At last, we prove the asymptoticnormality of unknown parameters.Chapter three, apply the statistical inference principles with partially missingdata to study the maximum likelihood estimation of the weighted index distribution inthe case of missing data, and prove the strong consistency and asymptotic normalityof estimators.Chapter four, using the method of weighted exponential distribution to research new Lomax distribution, we also obtain the corresponding properties and conclusion.