The Generalized T-Distribution And Its Applications

In modem statistical theory, many statistical distributions and their properties are stud-ied. When traditional distributions can't meet our requirements, we have to seek for new ones. We can easily find that statistical methods are used much more frequently in modem economy and industry fields, thus it is very important to do research on methods of fitting data. Usually we use normal distribution, t-distribution and exponential distribution to fit data. But nowadays we can usually find out a situation that some data own some skewness but not symmetry. This fact illustrates that it's not appropriate to fit these data by normal distribution or t-distribution any more, and we must seek new distributions to deal with these new skewness and finally model data more precisely.The purpose of this article is to generalize a familiar distribution-t-distribution, we hope the new one can fit skewness in the datasets. By using some usual methods. we finally get a new distribution-generalized t-distribution, which contains some good properties such as the property of skewness. And the traditional t-distribution is a particular one of the new family.Based on< A New Skew Generalization of The Normal Distribution:Properties and Applications>[28], the author uses the method of inserting a new parameter to generalize the traditional normal distribution, and get a new one-generalized normal distribution. By using a similar method, here I am going to generalize the traditional t-distribution with a degree n, and study properties of the new one. After this, we can estimate its parameters more easily. In the article, some examples are introduced to illustrate its extensive application range. The examples include a contrast between the estimators of parameters and the real ones.By introducing the generalized t-distribution, we extend the quantities of distributions, and it can be used to model skewness in data, which makes the fitting of data more conve-niently and practically.