Almost sure limit theorems for random sums of multiindex random variables

2009 ◽  
Vol 49 (3) ◽  
pp. 318-330
Author(s):  
L. P. Terekhova
Keyword(s):  
Limit Theorems ◽  
Random Variables ◽  
Random Sums ◽  
Almost Sure Limit Theorems

Almost sure limit theorems for random allocations

2005 ◽  
Vol 42 (2) ◽  
pp. 173-194
Author(s):  
István Fazekas ◽  
Alexey Chuprunov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Domain ◽  
Almost Sure Limit Theorem ◽  
The Central Limit Theorem ◽  
Almost Sure Limit Theorems ◽  
Poisson Limit

Almost sure limit theorems are presented for random allocations. A general almost sure limit theorem is proved for arrays of random variables. It is applied to obtain almost sure versions of the central limit theorem for the number of empty boxes when the parameters are in the central domain. Almost sure versions of the Poisson limit theorem in the left domain are also proved.

scholarly journals On chi-square type distributions with geometric degrees of freedom in relation to geometric sums

2019 ◽  
Vol 22 (1) ◽  
pp. 180-184
Author(s):  
Tran Loc Hung
Keyword(s):  
Degrees Of Freedom ◽  
Limit Theorems ◽  
Random Variables ◽  
Weak Limit ◽  
Random Sums ◽  
Chi Square ◽  
Asymptotic Behaviors ◽  
Weak Limit Theorems ◽  
Geometric Sums ◽  
Applied Fields

The chi-square distribution with degrees of freedom has an important role in probability, statistics and various applied fields as a special probability distribution. This paper concerns the relations between geometric random sums and chi-square type distributions whose degrees of freedom are geometric random variables. Some characterizations of chi-square type random variables with geometric degrees of freedom are calculated. Moreover, several weak limit theorems for the sequences of chi-square type random variables with geometric random degrees of freedom are established via asymptotic behaviors of normalized geometric random sums.

scholarly journals Random sums of random vectors and multitype families of productive individuals

2004 ◽  
Vol 2004 (19) ◽  
pp. 975-990
Author(s):  
I. Rahimov ◽  
H. Muttlak
Keyword(s):  
Stochastic Processes ◽  
Special Form ◽  
Limit Theorems ◽  
Random Variables ◽  
Random Sums ◽  
Random Vectors ◽  
Bernoulli Random Variables

We prove limit theorems for a family of random vectors whose coordinates are a special form of random sums of Bernoulli random variables. Applying these limit theorems, we study the number of productive individuals inn-type indecomposable critical branching stochastic processes with types of individualsT1,…,Tn.

A study of chi-square-type distribution with geometrically distributed degrees of freedom in relation to distributions of geometric random sums

2020 ◽  
Vol 70 (1) ◽  
pp. 213-232
Author(s):  
Tran Loc Hung
Keyword(s):  
Degrees Of Freedom ◽  
Limit Theorems ◽  
Random Variables ◽  
Weak Limit ◽  
Sums Of Squares ◽  
Random Sums ◽  
Chi Square ◽  
Type Distribution ◽  
Standard Normal ◽  
Weak Limit Theorems

AbstractThe purpose of this paper is to study a chi-square-type distribution who degrees of freedom are geometric random variables in connection with weak limiting distributions of geometric random sums of squares of independent, standard normal distributed random variables. Some characteristics of chi-square-type random variables with geometrically distributed degrees of freedom including probability density function, probability distribution function, mean and variance are calculated. Some asymptotic behaviors of chi-square-type random variables with geometrically distributed degrees of freedom are also established via weak limit theorems for normalized geometric random sums of squares of independent, standard normal distributed random variables. The rates of convergence in desired weak limit theorems also estimated through Trotter’s distance. The received results are extensions and generalizations of several known results.

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