PROBABILISTIC-GEOMETRIC THEOREMS ARISING FROM THE ANALYSIS OF CONTINGENCY TABLES

摘要: Publisher Summary This chapter presents a geometric explanation for the similarity of two classical formulas in probability: Stevens's formula chance that n random arcs cover circle and Laplace's density sum uniform variables. Probabilistic-geometric proofs de Finettiss distribution function point on n-simplex, an extension Bayesss result—a mixture multinomials has Bose-Einstein distribution, result Stanley explaining why permutation k or fewer rising sequences can be expressed terms formula. The generalized variance vector is defined to product nonzero eigenvalues its covariance matrix. Simple are derived multinomial Dirichlet distributions, Fisher-Yates distribution. latter multivariate version hypergeometric