scholarly journals Some inequalities of linear combinations of independent random variables: II

Bernoulli ◽  
2013 ◽  
Vol 19 (5A) ◽  
pp. 1776-1789 ◽  
Author(s):  
Xiaoqing Pan ◽  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Linear Combinations

scholarly journals A bound on the Wasserstein-2 distance between linear combinations of independent random variables

2019 ◽  
Vol 129 (7) ◽  
pp. 2341-2375 ◽  
Author(s):  
Benjamin Arras ◽  
Ehsan Azmoodeh ◽  
Guillaume Poly ◽  
Yvik Swan
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Linear Combinations

scholarly journals Some Inequalities of Linear Combinations of Independent Random Variables. I.

2011 ◽  
Vol 48 (4) ◽  
pp. 1179-1188 ◽  
Author(s):  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Sufficient Condition ◽  
Linear Combinations ◽  
Heavy Tailed

In this paper we provide some sufficient conditions to stochastically compare linear combinations of independent random variables. The main results extend those given in Proschan (1965), Ma (1998), Zhao et al. (2011), and Yu (2011). In particular, we propose a new sufficient condition to compare the peakedness of linear combinations of independent random variables which may have heavy-tailed properties.

scholarly journals Some Inequalities of Linear Combinations of Independent Random Variables. I.

2011 ◽  
Vol 48 (04) ◽  
pp. 1179-1188 ◽  
Author(s):  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Sufficient Condition ◽  
Linear Combinations ◽  
Heavy Tailed

In this paper we provide some sufficient conditions to stochastically compare linear combinations of independent random variables. The main results extend those given in Proschan (1965), Ma (1998), Zhao et al. (2011), and Yu (2011). In particular, we propose a new sufficient condition to compare the peakedness of linear combinations of independent random variables which may have heavy-tailed properties.

ON ORDERINGS BETWEEN WEIGHTED SUMS OF RANDOM VARIABLES

2012 ◽  
Vol 27 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Tiantian Mao ◽  
Xiaoqing Pan ◽  
Taizhong Hu
Keyword(s):  
Likelihood Ratio ◽  
Random Variables ◽  
Hazard Ratio ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Linear Combinations ◽  
Sums Of Random Variables ◽  
General Setup

Linear combinations of independent random variables have been extensively studied in the literature. Xu & Hu [21] and Pan, Xu, & Hu [16] unified the study of linear combinations of independent random variables under the general setup. This paper is a companion one of these two papers. In this paper, we will further study this topic. The results are further generalized to the cases of permutation invariant random variables and of independent but not necessarily identically distributed random variables which are ordered in the likelihood ratio or the hazard ratio order.

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Methodology of Calculation the Terminal Settling Velocity Distribution of Irregular Particles for High Values of the Reynold’s Number/Metodologia Wyliczania Rozkładu Granicznej Prędkości Opadania Ziaren Nieregularnych Dla Wysokich Wartości Liczb Reynoldsa

2014 ◽  
Vol 59 (2) ◽  
pp. 553-562 ◽  
Author(s):  
Agnieszka Surowiak ◽  
Marian Brożek
Keyword(s):  
Velocity Distribution ◽  
Settling Velocity ◽  
Random Variables ◽  
Independent Random Variables ◽  
Calculation Algorithm ◽  
Shape Coefficient ◽  
Geometrical Properties ◽  
Size And Shape ◽  
Physical Density ◽  
Settling Velocity Distribution

Abstract Settling velocity of particles, which is the main parameter of jig separation, is affected by physical (density) and the geometrical properties (size and shape) of particles. The authors worked out a calculation algorithm of particles settling velocity distribution for irregular particles assuming that the density of particles, their size and shape constitute independent random variables of fixed distributions. Applying theorems of probability, concerning distributions function of random variables, the authors present general formula of probability density function of settling velocity irregular particles for the turbulent motion. The distributions of settling velocity of irregular particles were calculated utilizing industrial sample. The measurements were executed and the histograms of distributions of volume and dynamic shape coefficient, were drawn. The separation accuracy was measured by the change of process imperfection of irregular particles in relation to spherical ones, resulting from the distribution of particles settling velocity.

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