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Exact laws for sums of ratios of order statistics from the Pareto distribution

100%

Adler A.

Open Mathematics

2006

tom 4

nr 1

1-4

Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).

The rate of convergence for spectra of GUE and LUE matrix ensembles

84%

Götze F., Tikhomirov A.

Open Mathematics

2005

tom 3

nr 4

666-704

We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.

Ograniczanie wyników

2 Open Mathematics

1 Adler A.

1 Götze F.

1 Tikhomirov A.

1 2006

1 2005

Wyniki wyszukiwania

Exact laws for sums of ratios of order statistics from the Pareto distribution

The rate of convergence for spectra of GUE and LUE matrix ensembles