Naomi Chana Brownstein, University of Central Florida


Transformation of Variables in Statistics

Abstract:  How many distributions are there in Statistics? By looking at any reference edition, one can find dozens of various distribution families. Usually, the inference is done separately for each distribution, requires a significant amount of effort, and often leads to errors in the results. In many case these efforts can be avoided by applying techniques related to transformation of random variables. These methods are used routinely in maximum likelihood estimation but are rarely applied in other statistical procedures.

In this project, we explored transformations of variables and applied them to derivations of the best unbiased estimators, Bayesian estimators, construction of various kinds of priors, estimation, and inference in the stress-strength problem.

First, we obtained general results on the application of transformations of random variables to the derivation of numerous statistical procedures. Second, we created a list of common distributions and the relationships between them. Third, we provided examples of applications of our theory. Namely, we took papers published in various statistical journals and obtained the same results in just a few lines with almost no effort. 

The value of this project is in the fact that by using only undergraduate level statistics, we obtained very powerful results.  Further application of these techniques will be described at the conference.


Undergraduate Mentor: Marianna Pensky (UCF)