Strong Laws of Large Numbers and Central Limit Theorems for Set-Valued Random Variables

2002 ◽  
pp. 87-115 ◽  
Author(s):  
Shoumei Li ◽  
Yukio Ogura ◽  
Vladik Kreinovich
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers

scholarly journals The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1192
Author(s):  
Li Guan ◽  
Juan Wei ◽  
Hui Min ◽  
Junfei Zhang
Keyword(s):  
Metric Space ◽  
Limit Theorems ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Fuzzy Metric Space ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Fuzzy Metric ◽  
Large Numbers ◽  
Definition Of

In this paper, we firstly introduce the definition of the fuzzy metric of sets, and discuss the properties of fuzzy metric induced by the Hausdorff metric. Then we prove the limit theorems for set-valued random variables in fuzzy metric space; the convergence is about fuzzy metric induced by the Hausdorff metric. The work is an extension from the classical results for set-valued random variables to fuzzy metric space.

Limit theorems for sums of general functions of m-spacings

1984 ◽  
Vol 96 (3) ◽  
pp. 517-532 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Asymptotic Properties ◽  
Central Limit Theorems ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Explicit Formulae ◽  
General Distributions

Laws of large numbers and central limit theorems are proved for sums of general functions of m-spacings from general distributions. Explicit formulae are given for the norming constants. The results enable us to describe asymptotic properties of distributional tests under fixed alternatives. A generalization of Kimball's spacings test is considered in detail.

Sign in / Sign up

Export Citation Format

Share Document