 ## Pence-Boyce STEM Student Scholarship

#### Title

Optimizing Percentile Matching

Summer 7-23-2021

Thesis

#### Department

Mathematics

Dr. Dale Hathaway

#### Abstract

Point estimation is a technique used in statistics to estimate unknown parameters in populations of data by using samples of data from that population. Percentile matching is a method of point estimation that selects one piece of data from a sample and assumes that the percentile that piece of data represents in the sample is equal to that same percentile’s theoretical value in the population. That assumption is then used to project what the unknown parameter is. The fundamental question our research sought to answer was which percentile should be matched from the sample to the population to produce the best point estimates for the exponential distribution. By evaluating percentiles that naturally occurred in samples, we were able to use order statistics to calculate the variance and expected value of error for point estimates created by different percentiles. We concluded that creating point estimates using the 80th percentile will consistently be optimal.

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