Estimation Of Change Point For Uniform Distribution Based On The Bayesian Method

ABSTRACT:The statistical analysis of change point becomes a novel but fast developing issue. In1954, the change point was first proposed by Page when he inspected the product quality in the auto-production line. Until1980’s, some researchers began to exp lore this issue combining with Bayesian method. But they mainly focused on the most common distributions such as exponential distribution family and so on. In this paper, we devote to discussing the detection of change point of another important distribution, namely uniform distribution.Firstly, a simple change point model with uniform distribution is proposed in order to offer a fundamental form of the research questions and the purpose of this paper, which focuses on the estimation of change point. Then, a variety of chosen methods on the prior distribution are introduced in the process of the model solution, including continuous uniformity null information prior distribution, discrete uniformity null information prior, generalized prior distribution, Jeffreys null information prior and conjugate prior distribution. Moreover, we introduce three different methods of estimation which are widely used to the estimation of hyper-parameters in classical statistics, which include method of moments, maximum likelihood estimate and ML-Ⅱ estimation based on Bayesian method. Using these estimations, the density function of posterior distribution is obtained and the location of the change point is estimated finally. Based on the theory which is mentioned above, we use the simulated data which is generated by Matlab to test the model and the results show that our method is rather effective. In the empirical research, the proposed method is applied to estimate the change point of the waiting-time data at one of the Beijing bus stations.