実際にポスターで発表したものは、さらにかなり更新されている。 国際産業数理・応用数理会議(2023-08-20〜2023-08-25)

1. Multiplying the absolute values from
Student's t-distribution of two degrees
produces the Bradley-Terry model
ICIAM 2023 TOKYO (10th International Congress on Industrial and Applied Mathematics) – 2023-08-25
Consider the Bradley-Terry model (1952) where each player i has a latent value πᵢ > 0 to
"beat" another player j with the probability πᵢ / (πᵢ + πⱼ). If one supposes "i beats j" occurs in
this model iff πᵢ |vᵢ| > πⱼ |vⱼ| with independent random variates vᵢ, vⱼ ~ D where D represents a
probability distribution, a solution of D is, interestingly, Student's t-distribution with 2 degrees
of freedom.
Toshiyuki Shimono
The condition upon x₁ and x₂ is equivalent to :
※ T and F mean Student’s t and Snedecor’s F distribution.
A uniform distribution
is yielded − mysteriously!
The theory herein may yield a methodology regarding how to “fairly” or “flexibly” produces/handles numerical
“strengths” of the bipartite society, as well as deepening the understanding of the multiplicative relations among
stochastic distributions.