scholarly journals A Note on the Central Limit Theorems for Dependent Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Distribution Functions ◽  
Central Limit Theorems ◽  
Cumulative Distribution ◽  
Characteristic Functions ◽  
Mixing Conditions ◽  
Cumulative Distribution Functions ◽  
Probability And Statistics

Classical central limit theorem is considered the heart of probability and statistics theory. Our interest in this paper is central limit theorems for functions of random variables under mixing conditions. We impose mixing conditions on the differences between the joint cumulative distribution functions and the product of the marginal cumulative distribution functions. By using characteristic functions, we obtain several limit theorems extending previous results.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

Central Limit Theorems for Interchangeable Processes

1958 ◽  
Vol 10 ◽  
pp. 222-229 ◽  
Author(s):  
J. R. Blum ◽  
H. Chernoff ◽  
M. Rosenblatt ◽  
H. Teicher
Keyword(s):  
Stochastic Process ◽  
Probability Measure ◽  
Central Limit ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Probability Measures ◽  
Image Position ◽  
Positive Integers

Let {Xn} (n = 1, 2 , …) be a stochastic process. The random variables comprising it or the process itself will be said to be interchangeable if, for any choice of distinct positive integers i 1, i 2, H 3 … , ik, the joint distribution of depends merely on k and is independent of the integers i 1, i 2, … , i k. It was shown by De Finetti (3) that the probability measure for any interchangeable process is a mixture of probability measures of processes each consisting of independent and identically distributed random variables.

Matrix variate pareto distributions

2021 ◽  
Vol 71 (2) ◽  
pp. 475-490
Author(s):  
Shokofeh Zinodiny ◽  
Saralees Nadarajah
Keyword(s):  
Distribution Functions ◽  
Cumulative Distribution ◽  
Characteristic Functions ◽  
Type I ◽  
Type Ii ◽  
Cumulative Distribution Functions ◽  
Pareto Distributions

Abstract Matrix variate generalizations of Pareto distributions are proposed. Several properties of these distributions including cumulative distribution functions, characteristic functions and relationship to matrix variate beta type I and matrix variate type II distributions are studied.

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