Riemann $R\sb{1}$-summability of independent, identically distributed random variables

Comparison of Sums of Independent Identically Distributed Random Variables

Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ‖Sk‖ with that of ‖Sj‖, and deduce some tail distribution maximal inequalities. The main result of this paper was inspired by the inequality from [dP–M] that says that Pr(‖X1‖ > t) ≤ 5 Pr(‖X1 +X2‖ > t/2) whenever X1 and X2 are independent...

Generating the Maximum of Independent Identically Distributed Random Variables

Frequently the need arises for the computer generation of variates that are exact/y distributed as 2 = max(X,, . , X.) where X,, . . . , X, form a sequence of independent identically distributed random variables. For large n the individual generation of the Xi’s is unfeasible, and the inversion-of-a-beta-variate is potentially inaccurate. In this paper, we discuss and compare the corrected inve...

Summability of Double Independent Random Variables

We will examine double sequence to double sequence transformation of independent identically distribution random variables with respect to four-dimensional summability matrix methods. The main goal of this paper is the presentation of the following theorem. If maxk,l|am,n,k,l| maxk,l|am,kan,l| O m−γ1 O n−γ2 , γ1, γ2 > 0, then E|X̆|1 1/γ1 < ∞ and E| ̆̆ X|1 1/γ2 < ∞ imply that Ym,n → μ almost sure P...

Distribution of the Maximum of Independent Identically-distributed Variables

Many engineering applications require the calculation of the distribution of the maximum of a number n of indendent, identically distributed (iid) variables. A typical situation is the design of a system for the “n-year demand” when the maximum demands in different years are iid (design of a dam for the n-year flood, design of an offshore platform for the n-year wave, design of a building for t...

Distribution of the Maximum of Independent Identically-distributed Variables