Strong and Weak Laws of Large Numbers for Weighted Sums of Fuzzy Set-Valued Random Variables

2004 ◽  
pp. 117-124
Author(s):  
Li Guan ◽  
Shoumei Li
Keyword(s):  
Fuzzy Set ◽  
Random Variables ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws

LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF FUZZY SET-VALUED RANDOM VARIABLES

2004 ◽  
Vol 12 (06) ◽  
pp. 811-825 ◽  
Author(s):  
LI GUAN ◽  
SHOUMEI LI
Keyword(s):  
Fuzzy Set ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Random Variable ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers

In this paper, we shall present weak and strong laws of large numbers (WLLN's and SLLN's) for weighted sums of independent (not necessarily identically distributed) fuzzy set-valued random variables in the sense of the extended Hausdorff metric [Formula: see text], based on the result of set-valued random variable obtained by Taylor and Inoue32,33. This work is a continuation of Li and Ogura20.

scholarly journals Limit theorems for randomly selected adjacent order statistics from a Pareto distribution

2005 ◽  
Vol 2005 (21) ◽  
pp. 3427-3441 ◽  
Author(s):  
André Adler
Keyword(s):  
Order Statistics ◽  
Prior Distribution ◽  
Limit Theorems ◽  
Pareto Distribution ◽  
Random Variables ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Weak Laws ◽  
Selection Of

Consider independent and identically distributed random variables{Xnk,  1≤k≤m, n≥1}from the Pareto distribution. We randomly select two adjacent order statistics from each row,Xn(i)andXn(i+1), where1≤i≤m−1. Then, we test to see whether or not strong and weak laws of large numbers with nonzero limits for weighted sums of the random variablesXn(i+1)/Xn(i)exist, where we place a prior distribution on the selection of each of these possible pairs of order statistics.

scholarly journals A note on convergence of weighted sums of random variables

1985 ◽  
Vol 8 (4) ◽  
pp. 805-812 ◽  
Author(s):  
Xiang Chen Wang ◽  
M. Bhaskara Rao
Keyword(s):  
Integrability Condition ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Uniform Integrability ◽  
Laws Of Large Numbers ◽  
Sums Of Random Variables ◽  
Large Numbers ◽  
Pairwise Independent Random Variables ◽  
Weak Laws

Under uniform integrability condition, some Weak Laws of large numbers are established for weighted sums of random variables generalizing results of Rohatgi, Pruitt and Khintchine. Some Strong Laws of Large Numbers are proved for weighted sums of pairwise independent random variables generalizing results of Jamison, Orey and Pruitt and Etemadi.

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