The Final Contributions of Samuel Kotz

• Activity Number: 53
• Type: Invited
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Memorial
• Author(s): Guillermina Jasso*+ and Johan Rene Van Dorp and Edith Seier
• Companies: New York University and The George Washington University and East Tennessee State University
• Keywords: bounded distributions ; kurtosis ; systems of distributions ; inequality ; social status ; happiness

Abstract

Samuel Kotz had an infinite curiosity about probability distributions -- the varieties of distributions, the systems for comparing and classifying them, and their endless insight for deepening understanding about the physical and social worlds. This paper summarizes three lines of inquiry which Kotz pursued with three collaborators. With Van Dorp, Kotz explored bounded distributions, whose relative scarcity contrasts sharply with the multitude of unbounded distributions. They have introduced a novel two-sided framework of bounded distributions of which their earliest contribution, the Two-Sided Power distribution (TSP), is a member. With Jasso, Kotz explored statistical aspects of mechanisms by which human characteristics generate status, together with the consequent contrasts between inequality in the characteristics and status inequality. They also analyzed new models of happiness. In both projects, they found new distributions. With Seier, Kotz published four papers on kurtosis, all in the period 2007-2008 and all advancing the framework for classifying distributions based on kurtosis. They were also systematizing additional questions on kurtosis that remain unexplored.