Couplings for Irregular Combinatorial Assemblies
When approximating the joint distribution of the component counts of a decomposable combinatorial structure that is ‘almost’ in the logarithmic class, but nonetheless has irregular structure, it is useful to be able first to establish that the distribution of a certain sum of non-negative integer valued random variables is smooth. This distribution is not like the normal, and individual summands can contribute a non-trivial amount to the whole, so its smoothness is somewhat surprising. In this paper, we consider two coupling approaches to establishing the smoothness, and contrast the results that are obtained.
KeywordsFailure Probability Independent Random Variable Probability Mass Function Coupling Approach Total Variation Distance
- 4.Barbour AD, Nietlispach B (2010) Approximation by the Dickman distribution and quasi–logarithmic combinatorial structures, arXiv:1007.5269Google Scholar
- 5.Knopfmacher J (1979) Analytic arithmetic of algebraic number fields Lecture notes in pure and applied mathematics. vol 50, Marcel Dekker, New YorkGoogle Scholar
- 7.Manstavicius E (2009). Strong convergence on weakly logarithmic combinatorial assemblies, arXiv:0903.1051Google Scholar
- 11.Vervaat W (1972) Success epochs in Bernoulli trials with applications in number theory. Mathematical centre tracts, vol 42. Mathematisch Centrum, AmsterdamGoogle Scholar