Geometric Processes And Repairable System

In this paper, we study the problem about statistical inference for geo-metric process. The paper consists of forth parts. Firstly, we introduce theconcept of geometric process (GP) and some fields of its applications. Sec-ondly, we introduce statistical inferrence for GP. Thirdly, we introduce themax likelihood estimation(MLE) of the geometric parameter and its consis-tence and asymptotic normality. It is difficult to solve the likelihood equationof geometric parameter. Lam Y. has studied the MLE of GP with lognor-mal distribution in 1988, simply because the solution of likelihood equationof geometric parameter can be derived. Finally, we give the idea to estimateparameter of the distribution.The important part of the paper is how to estimate parameter of thedistribution. A stochastic process {X₁,…, X_n} is GP, Let f(·) be the density ofX₁ , when f(·) is unknown, in certain condition, how to estimate parameter ofthe distribution. It is very useful for solving practical problems. Furthermore,When {X₁,…,X_n} is i.i.d, we give the idea to estimate parameter of thedistribution.