Graduation Year
2011
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Nicholas Pippenger
Reader 2
Francis Edward Su
Terms of Use & License Information
Rights Information
© 2011 Kyle Luh
Abstract
Wassily Hoeffding, in his 1963 paper, introduces a procedure to derive inequalities between distributions. This method relies on finding a martingale coupling between the two random variables. I have developed a construction that establishes such couplings in various urn models. I use this construction to prove the inequality between the hypergeometric and binomial random variables that appears in Hoeffding's paper. I have then used and extended my urn construction to create new inequalities.
Recommended Citation
Luh, Kyle, "Martingale Couplings and Bounds on Tails of Probability Distributions" (2011). HMC Senior Theses. 7.
https://scholarship.claremont.edu/hmc_theses/7
