# Search Results

## You are looking at 1 - 10 of 22 items for :

• "linear combinations"
• All content
Clear All

# A note on asymptotics of linear combinations of iid random variables

Periodica Mathematica Hungarica
Author: Péter Kevei

## Abstract

Let X1,X2, ... be iid random variables, and let a n = (a 1,n, ..., a n,n) be an arbitrary sequence of weights. We investigate the asymptotic distribution of the linear combination

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$S_{a_n }$$ \end{document}
= a 1,n X 1 + ... + a n,n X n under the natural negligibility condition limn→∞ max{|a k,n|: k = 1, ..., n} = 0. We prove that if
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$S_{a_n }$$ \end{document}
is asymptotically normal for a weight sequence a n, in which the components are of the same magnitude, then the common distribution belongs to
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{D}$$ \end{document}
(2).

Restricted access

# Asymptotic distributions of linear combinations of intermediate order statistics

Acta Mathematica Hungarica
Author: L. Viharos
Restricted access

# On approximation of unbounded functions by linear combinations of modified Szász-Mirakian operators

Acta Mathematica Hungarica
Author: H. S. Kasana
Restricted access

# Merging asymptotic expansions for cooperative gamblers in generalized St. Petersburg games

Acta Mathematica Hungarica
Authors: S. Csörgő and P. Kevei

## Abstract

Merging asymptotic expansions are established for the distribution functions of suitably centered and normed linear combinations of winnings in a full sequence of generalized St. Petersburg games, where a linear combination is viewed as the share of any one of n cooperative gamblers who play with a pooling strategy. The expansions are given in terms of Fourier-Stieltjes transforms and are constructed from suitably chosen members of the classes of subsequential semistable infinitely divisible asymptotic distributions for the total winnings of the n players and from their pooling strategy, where the classes themselves are determined by the two parameters of the game. For all values of the tail parameter, the expansions yield best possible rates of uniform merge. Surprisingly, it turns out that for a subclass of strategies, not containing the averaging uniform strategy, our merging approximations reduce to asymptotic expansions of the usual type, derived from a proper limiting distribution. The Fourier-Stieltjes transforms are shown to be numerically invertible in general and it is also demonstrated that the merging expansions provide excellent approximations even for very small n.

Restricted access

# On the linear combination of q -additive functions at prime places

Acta Mathematica Hungarica
Author: I. Kátai

## Abstract

Necessary and sufficient conditions are given for linear combinations of q-ary additive functions to belong to some function classes when the summation is extended to the set of primes.

Restricted access

# Weak laws of large numbers for cooperative gamblers

Periodica Mathematica Hungarica
Authors: Sándor Csörgő and Gordon Simons

## Abstract

Based on a stochastic extension of Karamata’s theory of slowly varying functions, necessary and sufficient conditions are established for weak laws of large numbers for arbitrary linear combinations of independent and identically distributed nonnegative random variables. The class of applicable distributions, herein described, extends beyond that for sample means, but even for sample means our theory offers new results concerning the characterization of explicit norming sequences. The general form of the latter characterization for linear combinations also yields a surprising new result in the theory of slow variation.

Restricted access

# Laws of large numbers for cooperative St. Petersburg gamblers

Periodica Mathematica Hungarica
Authors: Sándor Csörgő and Gordon Simons

Summary General linear combinations of independent winnings in generalized \St~Petersburg games are interpreted as individual gains that result from pooling strategies of different cooperative players. A weak law of large numbers is proved for all such combinations, along with some almost sure results for the smallest and largest accumulation points, and a considerable body of earlier literature is fitted into this cooperative framework. Corresponding weak laws are also established, both conditionally and unconditionally, for random pooling strategies.

Restricted access

# Multivariate statistical analysis of the bibliographic output from a research institution, in relation to the measures of scientific policy

Scientometrics
Authors: Vl. Simeon, B. Momčilović, Z. Kralj, and B. Grgas

## Abstract

The publications produced in a medical research institute in a 16 year interval were classified into five categories (scientific papers in the journals covered byCurrent Contents orScience Citation Index, scientific papers in other journals, books and monographs, technical papers, congress and symposia communications) and counted for each year separately. The number of researchers and yearly budgets were also recorded. The data were analysed by contingency table, correlation and factor-analytical methods. It was shown that, upon introducing quantitative minimal criteria for job promotions, the proportion of scientific papers increased. Principal component analysis indicated that the data can be approximately represented as linear combinations of three mutually independent factors. The approach used is recommended for evaluating the production of scientific information in research institutions and for assessing the effects of the measures of scientific policy.

Restricted access

# Direct estimate on pointwise simultaneous approximation by combinations of Baskakov operators

Studia Scientiarum Mathematicarum Hungarica
Authors: Linsen Xie and Xiaoping Zhang

combinations of Bernstein operators, J. Approx. Theory 107 (2000), 109–120. MR 2001h :41036 Song Z. J. Pointwise approximation for linear combinations of Bernstein operators

Restricted access

# Simultaneous approximation by combinations of Bernstein–Kantorovich operators

Acta Mathematica Hungarica
Authors: Li Cheng and Linsen Xie

.1007/978-1-4612-4778-4 . [6] Guo , S. S. Li , C. X. Liu , X. W. Song , Z. J. 2000 Pointwise approximation for linear combinations of Bernstein

Restricted access