Research Recap for Nov. 22: A Mathematics student and Statistics associate professor team up for an article in the American Statistician and research on migratory capabilities of alpine flora
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Kimihiro Noguchi and Koby Robles
A recent research article published in The American Statistician by Associate Professor of Statistics Kimihiro Noguchi and a fifth-year Mathematics undergraduate student Koby Robles fully characterizes distributions with the memoryless property, a well-known distributional property covered in typical undergraduate probability and statistics courses.
The memoryless property is a paradoxical phenomenon which is often explained in terms of the waiting time. Let's say that you just arrived at the bus stop. Then, the probability of a bus getting there in 3 minutes is the same as getting there in 10 minutes given that 7 minutes have already passed, or 23 minutes given that 20 minutes have already passed.
Previously, only two kinds of distributions, namely, the exponential and geometric distributions, are known to have the memoryless property. However, the article, titled "On generating distributions with the memoryless property," proposes a new algorithm which uniquely generates any distribution with the memoryless property. The algorithm only requires two ingredients; a positive parameter value and a set of values for which the distribution can take. The set of values must be closed under addition and have zero as the minimum. The article then illustrates several new types of distributions with the memoryless property and their real-life applications.
The project started after Robles came up with a highly original solution to the midterm question about the exponential distribution where he used the Poisson distribution instead. Sometimes, a research opportunity arises when it is not expected. However, that cannot be overlooked as it may end up rewriting the textbooks.
LiAn Noonan is a second-year grad student of Biology who studies endemic alpine flora in the Sierra Nevada and Southern Cascades. Noonan is a recipient of the Fraser & Hodgson Family Fellowship and the WWU Graduate Research Award for her thesis project titled, “Continuity of Floristics in the Alpine Zone of the Cascade-Sierran Axis: Is there a Continuum?” Noonan is interested in whether flora from the Sierra Nevada have the potential to migrate in response to climate change.
At the heart of Noonan’s research is an interest in conservation efforts on behalf of alpine endemic flora. Noonan says understanding flora’s capability to migrate is crucial for conservation efforts because they’re not capable of adapting in time to survive climate fluctuations. So, identifying potential regions of conservational priority for these endemic species is a big step in the right direction.
Noonan hopes to continue her work in conservation by extending her research with a follow-up study on dispersal barriers. Her faculty advisors are Instructor Mike Williams, Professor of Biology Ben Miner, and Assistant Professor of Biology Matthew Zinkgraf.