| Title |
Construction of the beta distributions using the random permutation divisors / |
| Authors |
Bareikis, Gintautas ; Manstavičius, Eugenijus |
| DOI |
10.15388/namc.2024.29.34009 |
| Full Text |
|
| Is Part of |
Nonlinear analysis: modelling and control.. Vilnius : Vilnius University Press. 2024, vol. 29, no. 2, p. 189-204.. ISSN 1392-5113. eISSN 2335-8963 |
| Keywords [eng] |
arcsine law ; Ewens distribution ; multiplicative function ; quasihypergeometric distribution ; random permutation |
| Abstract [eng] |
A subset of cycles comprising a permutation σ in the symmetric group Sn, n ∈ N, is called a divisor of σ. Then the partial sums over divisors with sizes up to un, 0 ≤ u ≤ 1, of values of a nonnegative multiplicative function on a random permutation define a stochastic process with nondecreasing trajectories. When normalized the latter is just a random distribution function supported by the unit interval. We establish that its expectations under various weighted probability measures defined on the subsets of Sn are quasihypergeometric distribution functions. Their limits as n -> 1 cover the class of two-parameter beta distributions. It is shown that, under appropriate conditions, the convergence rate is of the negative power of n order. |
| Published |
Vilnius : Vilnius University Press |
| Type |
Journal article |
| Language |
English |
| Publication date |
2024 |
| CC license |
|
