Statistical Analysis Of Two Kinds Of Evenly Distributed Distributions

This thesis proposes two parameter distributions that have some similar natures to uniform distribution and defines them as SU Ⅰ(θ1,θ2)(similar uniform distribution Ⅰ)and SU Ⅱ(θ1,θ2)(similar uniform distribution Ⅱ). Aiming at the two distributions, it carries out related statistical analyses. Specific work includes the following aspects.(1) It implements parameter moment estimation and maximum likelihood estimation (MLE) on two distributions on the occasion of full samples, and provides detailed theoretical basis for existence of MLE of SU Ⅰ(θ1,02) distribution and calculation of moment estimation of SU Ⅱ(θ1,θ2) distribution. Meanwhile, it uses Monte-Carlo simulation to compare superiority of each estimation on respective parameters of the two distributions, respectively.(2) It discusses nature of order statistics of the two distributions, such as distribution of order statistics and numerical characteristics of maximum and minimum statistics of the two distributions, and offers detailed theoretical description.(3) It not only discusses related nature of X(1),X(2)-X(1) of the two distributions and TP2dependency and RCSI of the two distributions but also gives specific theoretical proof.