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Application of Transformations
in Parametric Inference

By: Naomi Brownstein
Mentor: Dr. Marianna Pensky

Abstract

One can apply transformations of random variables to conduct inference for multiple distributions in a few simple steps. These methods are used routinely in maximum likelihood estimation but are rarely applied in other statistical procedures. In this project, transformations of variables were explored and applied to derivations of the best unbiased estimators, Bayesian estimators, construction of various kinds of priors, estimation and inference in the stress-strength problem. First, general results were obtained on the application of transformations of random variables to the derivation of numerous statistical procedures. Second, common distributions and the relationships between them were listed in a table. Third, examples of applications of our theory were provided; i.e., papers published in various statistical journals were examined and the same results were obtained in just a few lines with almost no effort. The value of this project lies in the fact that undergraduate level statistics can yield such powerful results.

Keywords: Transformations of Variables, Statistical Inference.

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