Western Washington University

03/18/2026 | News release | Distributed by Public on 03/18/2026 15:28

WWU Mathematics senior Cayden Lukken publishes statistics research, a ‘rare’ feat for undergraduate students

WWU Mathematics senior Cayden Lukken publishes statistics research, a 'rare' feat for undergraduate students

March 18, 2026

by Mikayla King

WWU Communications

Mathematics senior Cayden Lukken was able to present his research at the American Mathematical Society's Joint Mathematics Meeting.

Mathematics senior Cayden Lukken, mathematics and data science alum Mayla Ward and Professor of Mathematics Kimihiro Noguchi have published their research on mathematical statistics.

Undergraduate research is a rare achievement in mathematics, Noguchi said.

"The hurdle for doing research in math is generally very high," he said. "That's because if you want to find something new in math, you have to have very specialized knowledge of mathematics, but oftentimes in undergraduate education the students don't get there."

Senior Cayden Lukken spent hours working through equations on a whiteboard in Bond Hall.

The paper, "Asymptotic optimality of the Wilson-Hilferty cube-root transformation on the gamma distribution for higher-order odd central moments," was published in the June 2026 edition of Statistics & Probability Letters.

The study focused on the cube-root transformation of the gamma distribution, which is performed to make data appear symmetric so that statistical analysis can be done in a reliable manner.

The cube-root transformation is crucial to analyzing data in a variety of disciplines, including engineering, environmental science and genetics, Lukken said.

Lukken was initially drawn to working with Noguchi on this research project because of its many applications and because it offered an opportunity to learn something new.

"I think that statistics is one of the most applicable disciplines in mathematics," he said. "This research is something that could be useful for other people, and that piqued my interest."

Professor of Mathematics (left) and mathematics senior Cayden Lukken visited Washington D.C. to present their research during the American Mathematical Society's Joint Mathematics Meeting.

Traditionally, the cube-root transformation on the gamma distribution has been justified using the Wilson-Hilferty approach which depends on the third central moment, but their approach could not easily generalize higher-order odd central moments due to increasing complexity.

Noguchi, Lukken and Ward used a novel efficient quantile-based approach to show that there is a more computationally efficient alternative to the Wilson-Hilferty approach for higher-order odd central moments. The work builds upon research performed by Noguchi and Ward, whose findings were also published while Ward was an undergraduate at Western in 2024.

After several hundred hours and countless equations written across dozens of whiteboards, Noguchi, Lukken Ward demonstrated that the cube-root transformation remains optimal when used for any odd central moment of order three or higher.

Lukken was able to take his findings to the American Mathematical Society's Joint Mathematics Meeting in Washington D.C. in January, where he presented his research during a poster session.

"It was super cool getting to see other people's research and have other people see my work and really understand it," Lukken said about the experience.

After graduating this spring, Lukken is returning to Western next year as a graduate student in the Mathematics Department.

Read Noguchi, Lukken and Ward's full paper on ScienceDirect, and find out more about mathematical research at Western on https://mathematics.wwu.edu/.

Mikayla King ('17) covers the College of Science and Engineering and Woodring College of Education for University Communications. Reach out to her with story ideas at [email protected].

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