Truncated data

This thesis deals with truncated distributions. Firstly, the case of the truncated normal distribution is analyzed in detail. Two estimation methods are described - method of moments and maximum likelihood - together with the discussion of their properties and confidence region construction. A more advanced method - Bayes estimator - is briefly presented. Secondly, the truncated gamma distribution is analyzed, however, in less detail than the normal case. The theoretical part is closed with a method for estimating truncation boundaries when not even those are known. Throughout the thesis, results from multiple articles by various authors are summarized and presented in a unified notation. The numerical part deals with the analysis of a real dataset, describing the height of soldiers in the U.S. Army. The built theory is transformed into R code and executed, indicating the correctness of our theoretical results.