Eulerian Numbers in Sorting Process and Discrete Probability Distribution Function
ソーティング過程に現れるEulerian 数と離散型確率分布

Takahiro TSUCHIYA, Nagatomo NAKAMURA
JSAI Technical Report, Type 2 SIG  
The purpose of this paper is to discuss the discrete probability distribution function induced from the modified bucket sorting. The distribution is related to the unique sequence called "Eulerian Numbers" proposed by Euler (1755). There are sensitive differences between a derivation process of our proposal and Eulerian numbers expressed as a number of permutation runs. Recurrence relation for the moments of the distribution is also given. The mean, variance and higher order cumulants are
more » ... d using the relation. The interesting results that the relationship among the proposed, normal and uniform distributions are shown by asymptotic expansion. The efficiency of the proposed method is illustrated through some numerical experiments.
doi:10.11517/jsaisigtwo.2008.dmsm-a801_04 fatcat:ucrn6iuzandehljxpzwowbqsgm