Ian Harris

Document Type

Honors Thesis

Abstract

When analyzing survival data, which involves such parameters as lifetime, censoring rate, and any number of covariates, we have several distributions to try to fit the study into a model. Among these are the exponential, the gamma, the lognormal, and the Weibull distributions. The problem with these distributions is that their parameter requirements are quite stiff and not flexible. So, if some parameters are even slightly off (or otherwise unknown), how would we be able to model the data and, better yet, see if the data falls outside the given distributions? That is where the generalized gamma distribution comes in. The beauty of this distribution is how malleable it is and how it can be used as a blanket distribution of sorts to catch datasets that fall outside the commonly used distributions. Using R software, we performed a simulation study in which we generated datasets under the generalized gamma distribution and compared different iterations of the simulated data to models of the different distributions in a likelihood ratio test to show the rejection rates of models whose parameters differ. As the number of generated generalized gamma datasets increased (50 to 300 to 500), the rejection rates among different parameters (Q=0 vs. Q=0.5 to name one) grew larger and larger whilst the fixed vs. fitted model comparisons of the same parameter grew closer and closer to a 5% rejection rate. With this as a background, we applied the generalized gamma distribution to a real dataset, whose parameters were unknown, to estimate its parameters. Although it didn’t fall into any of the special cases, it still could fit in the generalized gamma distribution.

Publication Date

5-1-2019

Language

English

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