The Comparison And Application Simulation Of Several Parameters Estimation

With the rapid development of the society as well as science and technology, the advent of the information age, people often need to collect large amounts of data and to extract the potentially valuable information from these random and uncertain data. the word “statistics” appears more and more frequent in our daily life, as the gradually deepening understanding of people to statistical laws and the Increasingly extensive and in-depth application to statistical methods, the application prospect of statistics will be more and more extensive in every fields of life.The two schools of international mathematical statistics are Classical theory and Bayesian theory and the mutual criticism and controversy never rest between them, what's more, a new statistical method developed on the basis of them which is the empirical Bayesian statistics. They have advantages and disadvantages, in practical problems, we need to apply different statistical methods for different situations. Currently, There are very few articles put these three together to research, so, in this article, we mainly use the classical statistical(maximum likelihood estimation), Bayesian statistics(no information priori estimation, hierarchical Bayesian estimation, expected Bayesian estimation), empirical Bayesian statistics(nonparametric and parameter empirical Bayesian estimation) to estimate the parameters of the Poisson distribution and use Matlab to simulation and analysis the estimated value. Additionally, this article describes the application of multilayer Bayesian estimation and empirical Bayesian statistics in the aspect of product reliability which is under the zero failure data and Linex loss function, using hierarchical Bayesian and expected Bayesian to estimate the parameters of the exponential distribution and use Matlab to simulation and analysis the estimated value.