scholarly journals On Error Bounds for Approximations to Multivariate Distributions II

2002 ◽  
Vol 32 (1) ◽  
pp. 57-69
Author(s):  
Bjørn Sundt ◽  
Raluca Vernic
Keyword(s):  
Error Bounds ◽  
Random Variables ◽  
Independent Random Variables ◽  
Multivariate Distributions ◽  
Dependent Random Variables ◽  
Linear Transforms ◽  
Original Distribution ◽  
Multivariate Bernoulli ◽  
Bernoulli Distributions

AbstractIn the present paper, we study error bounds for approximations to multivariate distributions. In particular, we discuss some general versions of compound multivariate distributions and look at distributions of dependent random variables constructed by linear transforms of independent random variables or vectors. Special attention is paid to the case when the support of the original distribution is restricted. We also look at some applications with multivariate Bernoulli distributions.

Some Inequalities of Partial Sums for Negatively Dependent Random Variables

2012 ◽  
Vol 195-196 ◽  
pp. 694-700
Author(s):  
Hai Wu Huang ◽  
Qun Ying Wu ◽  
Guang Ming Deng
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Exponential Inequalities ◽  
Dependent Random Variables ◽  
Probability Inequalities ◽  
Associated Random Variables ◽  
Negatively Dependent Random Variables

The main purpose of this paper is to investigate some properties of partial sums for negatively dependent random variables. By using some special numerical functions, and we get some probability inequalities and exponential inequalities of partial sums, which generalize the corresponding results for independent random variables and associated random variables. At last, exponential inequalities and Bernsteins inequality for negatively dependent random variables are presented.

scholarly journals Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Aiting Shen
Keyword(s):  
Strong Consistency ◽  
Nearest Neighbor ◽  
Type Inequality ◽  
Random Variables ◽  
Independent Random Variables ◽  
Bernstein Type ◽  
Dependent Random Variables ◽  
Bernstein Type Inequality ◽  
Dependent Sequence ◽  
Fixed Design Regression

We present the Bernstein-type inequality for widely dependent random variables. By using the Bernstein-type inequality and the truncated method, we further study the strong consistency of estimator of fixed design regression model under widely dependent random variables, which generalizes the corresponding one of independent random variables. As an application, the strong consistency for the nearest neighbor estimator is obtained.

A simultaneous characterization of the Poisson and bernoulli distributions

1981 ◽  
Vol 18 (1) ◽  
pp. 316-320 ◽  
Author(s):  
George Kimeldorf ◽  
Detlef Plachky ◽  
Allan R. Sampson
Keyword(s):  
Poisson Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Constant Independent ◽  
Bernoulli Distribution ◽  
Bernoulli Distributions

Let N, X1, X2, · ·· be non-constant independent random variables with X1, X2, · ·· being identically distributed and N being non-negative and integer-valued. It is shown that the independence of and implies that the Xi's have a Bernoulli distribution and N has a Poisson distribution. Other related characterization results are considered.

On the asymptotic independent representations for sums of some weakly dependent random variables

2006 ◽  
Vol 43 (1) ◽  
pp. 33-46
Author(s):  
Rafik Aguech ◽  
Sana Louhichi ◽  
Sofyen Louhichi
Keyword(s):  
Positive Integer ◽  
Random Variables ◽  
Triangular Array ◽  
Independent Random Variables ◽  
Dependent Random Variables ◽  
Limiting Behavior ◽  
Weakly Dependent Random Variables ◽  
Weakly Dependent

Let, for each n?N, (Xi,n)0?i?nbe a triangular array of stationary, centered, square integrable and associated real valued random variables satisfying the weakly dependence condition lim N?N0limsup n?+8nSr=NnCov (X0,n, Xr,n)=0;where N0is either infinite or the first positive integer Nfor which the limit of the sum nSr=NnCov (X0,n, Xr,n) vanishes as n goes to infinity. The purpose of this paper is to build, from (Xi,n)0?i?n, a sequence of independent random variables (X˜i,n)0?i?nsuch that the two sumsSi=1nXi,nandSi=1nX˜i,nhave the same asymptotic limiting behavior (in distribution).

scholarly journals Moment inequality of the minimum for nonnegative negatively orthant dependent random variables

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1475-1481
Author(s):  
Xuejun Wang ◽  
Shijie Wang ◽  
Shuhe Hu
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Exponential Inequality ◽  
Moment Inequalities ◽  
Moment Inequality ◽  
Dependent Random Variables ◽  
The Moment

Let {xn,n ? 1} be a sequence of positive numbers and {?n,n ? 1} be a sequence of nonnegative negatively orthant dependent (NOD) random variables satisfying certain distribution conditions. An exponential inequality for the minimum min1?i?n xi?i is given. In addition, the moment inequalities of the minimum (Ek - min1?i?n|xi?i|p)1/p for nonnegative negatively orthant dependent random variables are established, where p > 0 and k = 1,2,..., n. Our results generalize the corresponding ones for independent random variables to the case of negatively orthant dependent random variables.

On the comparison of Shapley values for variance and standard deviation games

2021 ◽  
Vol 58 (3) ◽  
pp. 609-620
Author(s):  
Marcello Galeotti ◽  
Giovanni Rabitti
Keyword(s):  
Standard Deviation ◽  
Arbitrary Number ◽  
Random Variables ◽  
Independent Random Variables ◽  
Dependent Random Variables ◽  
Shapley Values

AbstractMotivated by the problem of variance allocation for the sum of dependent random variables, Colini-Baldeschi, Scarsini and Vaccari (2018) recently introduced Shapley values for variance and standard deviation games. These Shapley values constitute a criterion satisfying nice properties useful for allocating the variance and the standard deviation of the sum of dependent random variables. However, since Shapley values are in general computationally demanding, Colini-Baldeschi, Scarsini and Vaccari also formulated a conjecture about the relation of the Shapley values of two games, which they proved for the case of two dependent random variables. In this work we prove that their conjecture holds true in the case of an arbitrary number of independent random variables but, at the same time, we provide counterexamples to the conjecture for the case of three dependent random variables.

A simultaneous characterization of the Poisson and bernoulli distributions

1981 ◽  
Vol 18 (01) ◽  
pp. 316-320 ◽  
Author(s):  
George Kimeldorf ◽  
Detlef Plachky ◽  
Allan R. Sampson
Keyword(s):  
Poisson Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Constant Independent ◽  
Bernoulli Distribution ◽  
Bernoulli Distributions

Let N, X 1, X 2, · ·· be non-constant independent random variables with X 1, X 2, · ·· being identically distributed and N being non-negative and integer-valued. It is shown that the independence of and implies that the Xi 's have a Bernoulli distribution and N has a Poisson distribution. Other related characterization results are considered.

scholarly journals Finite algebras of Bernoulli distributions

2019 ◽  
Vol 29 (4) ◽  
pp. 267-276
Author(s):  
Alexey D. Yashunsky
Keyword(s):  
Boolean Functions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Finite Algebras ◽  
Bernoulli Distributions

Abstract The paper is concerned with sets of Bernoulli distributions which are closed under substitutions of independent random variables into Boolean functions from a given set (an algebra of Bernoulli distributions). A description of all finite algebras of Bernoulli distributions is given.

scholarly journals On Complete Convergence for Weighted Sums of Arrays of Dependent Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Soo Hak Sung
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Negatively Associated ◽  
Negatively Dependent Random Variables ◽  
Rowwise Independent ◽  
Mixing Random Variables

A rate of complete convergence for weighted sums of arrays of rowwise independent random variables was obtained by Sung and Volodin (2011). In this paper, we extend this result to negatively associated and negatively dependent random variables. Similar results for sequences ofφ-mixing andρ*-mixing random variables are also obtained. Our results improve and generalize the results of Baek et al. (2008), Kuczmaszewska (2009), and Wang et al. (2010).

scholarly journals Mathematical Models of Geometric Sizes of Cereal Crops’ Seeds as Dependent Random Variables

2018 ◽  
Vol 21 (3) ◽  
pp. 100-104 ◽  
Author(s):  
Roman Kuzm Inskyi ◽  
Stefan Kovalishyn ◽  
Yurij Kovalchyk ◽  
Roman Sheremeta
Keyword(s):  
Mathematical Models ◽  
Normal Distribution ◽  
Random Variables ◽  
Correlation Coefficients ◽  
Independent Random Variables ◽  
Cereal Crops ◽  
Density Functions ◽  
Dependent Random Variables ◽  
Data Approximation ◽  
Wheat Seeds

Abstract Dimensions of 100 randomly selected wheat seeds of the Smuglyanka variety, rye seeds of the Puhovchanka variety and barley seeds of the Pejas variety were determined by measuring their length (l), width (b) and thickness (h). Results of the measurements were processed by the methods of mathematical statistics; parameters of distributions of individual sizes as random variables were calculated. On the basis of values of variation coefficient, the density function of normal distribution (Gaussian distribution) was taken as a model of individual sizes of seeds. Models of two-dimensional distributions of seed sizes as independent random variables were presented. Correlation coefficients between geometric sizes of seeds were calculated. Obtained values of the correlation coefficients indicate that the geometric sizes of seeds should be considered as dependent random variables. Mathematical models of geometric sizes of studied cereal crops’ seeds as dependent random variables in the form of density functions of their normal distribution were proposed. By values of the sums of squared deviations as a fitting criterion, it was established that the mathematical models of geometric sizes of seeds as dependent random variables in the form of density functions of their normal distribution provide better data approximation than the mathematical models of geometric sizes of some cereal crops’ seeds as independent random variables.

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