Some Properties For Statistics Of Uniform And Exponential Distributions

In this paper, we derive some properties for statistics of two kinds of common probabil-ity distributions which are uniform and exponential distributions. We adopt a step-by-step approach whereby we first study the statistics of uniform and exponential distributions and then we make a analysis of statistics of mixture distribution which is related to uniform and exponential distributions.In the first chapter, we make a brief introduction on the background and importance of statistics of uniform and exponential distributions.In the second chapter, we analyze statistics of uniform distribution. In the first section, we construct the statistic which is used to represent estimate of interval center of uniform distribution, then find the large deviation and moderate deviation principles. In the second section, we derive properties for statistics which are three kinds of ratios of order statistics from uniform distribution, such as density function, expectation and variance, then we find some limit theorems.In the third chapter, we establish the central limit theorem and the almost sure central limit theorem for the statistic which is the ratio of the third order statistic and the second order statistic from exponential distribution.In the fourth chapter, we give definition of mixture distribution which is related to uni-form and exponential distributions and construct the statistics which are used to represent moment estimates of parameters, then find the asymptotic behavior.