Statistical Inference And Application Of Laplace Distribution

The Laplace distribution is one of the commonly-used distribution for probabilistic models.Laplace distribution plays an important role in securities investment and finance.In engineering,the processing of surveying and mapping data,as well as in the fields of voice and image data are also widely used.Therefore,the study on Laplace distribution is of great significance.The test of goodness of fit is a common problem in statistical applications,that is,whether a group of observations can be viewed as from a given population.We can use the background knowledge,sample data and sampling method to try to analyze and surmise this distribution,then the sample data is used to further test the distribution for probabilistic models.Therefore,the test of goodness of fit has an important application in life,economy,physics,chemistry and so on.This paper focuses on the study of Laplace distribution,discusses the main properties of it and their relation with other distribution.Then this paper mainly about its goodness of fit and introduces the basic properties of the Laplace distribution,test of goodness of fit of the two methods of common test of goodness of fit and Kolmogorov-Smimov test.Then we propose a new test statistic for the goodness of fit.Finally this paper uses MATLAB to compare the pros and cons of the three estimation methods.Finally,this paper discusses in the paper on the general nonlinear model by Laplace distribution and EM algorithm for least squares estimate,and the corresponding program by MATLAB design for relevant data simulation and analysis,to prove the effectiveness and robustness of this method...