| Title |
On a variance related to the Ewens sampling formula / |
| Authors |
Manstavičius, Eugenijus ; Žilinskas, Žydrūnas |
| DOI |
10.15388/NA.16.4.14088 |
| Full Text |
|
| Is Part of |
Nonlinear analysis : modelling and control.. Vilnius : Institute of Mathematics and Informatics. 2011, vol. 16, no. 4, p. 453-466.. ISSN 1392-5113 |
| Keywords [eng] |
Random permutation ; Cycle structure ; Integral operator ; Matrix eigenvalue ; Jacobi polynomial |
| Abstract [eng] |
A one-parameter multivariate distribution, called the Ewens sampling formula, was introduced in 1972 to model the mutation phenomenon in genetics. The case discussed in this note goes back to Lynch’s theorem in the random binary search tree theory. We examine an additive statistics, being a sum of dependent random variables, and find an upper bound of its variance in terms of the sum of variances of summands. The asymptotically best constant in this estimate is established as the dimension increases. The approach is based on approximation of the extremal eigenvalues of appropriate integral operators and matrices. |
| Published |
Vilnius : Institute of Mathematics and Informatics |
| Type |
Journal article |
| Language |
English |
| Publication date |
2011 |
| CC license |
|
