scholarly journals The nonuniform estimate of the convergence rate of the k-th maxima

2009 ◽  
Vol 50 ◽  
Author(s):  
Arvydas Jokimaitis
Keyword(s):  
Convergence Rate ◽  
Random Variables ◽  
Nonuniform Estimate ◽  
Kth Maxima ◽  
Independent Identically Distributed

In this paper the nonuniform estimate of the convergence rate for the kth maxima of the independent identically distributed random variables is obtained.

scholarly journals Estimation of Convergence Rate in the Transfer Theorem for Maxima

2008 ◽  
Vol 13 (1) ◽  
pp. 3-7
Author(s):  
A. Aksomaitis
Keyword(s):  
Convergence Rate ◽  
Random Variables ◽  
Nonuniform Estimate ◽  
Transfer Theorem ◽  
Independent Identically Distributed ◽  
Estimate Of Convergence Rate

Let ZN be a maximum of independent identically distributed random variables. In this paper, a nonuniform estimate of convergence rate in the transfer theorem max-scheme is obtained. Presented results make the estimates, given in [1] and [2], more precise.

Asymptotics of the Joint Distribution of Multivariate Extrema

2001 ◽  
Vol 6 (1) ◽  
pp. 3-8
Author(s):  
A. Aksomaitis ◽  
A. Jokimaitis
Keyword(s):  
Distribution Function ◽  
Convergence Rate ◽  
Joint Distribution ◽  
Random Variables ◽  
Nonuniform Estimate ◽  
Independent Identically Distributed ◽  
Estimate Of Convergence Rate

Let Wn and Zn be a bivariate extrema of independent identically distributed bivariate random variables with a distribution function F. in this paper the nonuniform estimate of convergence rate of the joint distribution of the normalized and centralized minima and maxima is obtained.

Nonuniform estimate of maximum density convergence rate for independent random variables

1999 ◽  
Vol 4 ◽  
pp. 3-9
Author(s):  
A. Aksomaitis ◽  
A. Jokimaitis
Keyword(s):  
Limit Theorem ◽  
Convergence Rate ◽  
Random Variables ◽  
Maximum Density ◽  
Independent Random Variables ◽  
Nonuniform Estimate ◽  
Density Limit ◽  
Estimate Of Convergence Rate

The nonuniform estimate of convergence rate in the maximum density limit theorem of independent nonidentically distributed random variables is obtained. This result is generalization of the work presented in [1].

scholarly journals The estimation of the convergence rate for maxima of random variables vectors

2010 ◽  
Vol 51 ◽  
Author(s):  
Lina Dindienė ◽  
Algimantas Aksomaitis
Keyword(s):  
Convergence Rate ◽  
Random Variables ◽  
Random Vectors ◽  
Nonuniform Estimate ◽  
Transfer Theorem ◽  
Independent And Identically Distributed

Linearly normalized maxima of independent and identically distributed random vectors is presented in this work. We’ve obtained nonuniform estimate of convergence in case when normalization is linear. For clearness there is given an example is this paper. Transfer theorem was aplied.

scholarly journals Discounted payments theorems for large deviations

2016 ◽  
Vol 57 ◽  
Author(s):  
Aurelija Kasparavičiūtė ◽  
Dovilė Deltuvienė
Keyword(s):  
Stochastic Process ◽  
Large Deviations ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Negative Integer ◽  
Nonuniform Estimate ◽  
Process With Independent Increments ◽  
Independent Increments ◽  
Independent Identically Distributed

  Let Z(t) = Σ j=1N(t) Xj, t ≥ 0, be a stochastic process, where Xj are independent identically distributed random variables, and N(t) is non-negative integer-valued process with independent increments. Throughout, we assume that N(t) and Xj are independent. The paper considers normal approximation to the distribution of properly centered and normed random variable Zδ =∫0∞e- δt dZ(t), δ > 0, taking into consideration large deviations both in the Cramér zone and the power Linnik zones. Also, we obtain a nonuniform estimate in the Berry–Essen inequality. 

A Note on the Accuracy of Normal Approximation of Random Quantities

2021 ◽  
Vol 73 (1) ◽  
pp. 62-67
Author(s):  
Ibrahim A. Ahmad ◽  
A. R. Mugdadi
Keyword(s):  
Sample Size ◽  
Order Statistic ◽  
Normal Approximation ◽  
Order Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Limiting Distribution ◽  
Exact Order ◽  
Fixed Sample ◽  
Independent Identically Distributed

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

scholarly journals A counterexample to the existence of a general central limit theorem for pairwise independent identically distributed random variables

2021 ◽  
Vol 499 (1) ◽  
pp. 124982
Author(s):  
Benjamin Avanzi ◽  
Guillaume Boglioni Beaulieu ◽  
Pierre Lafaye de Micheaux ◽  
Frédéric Ouimet ◽  
Bernard Wong
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Independent Identically Distributed
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