A remark on stable sequences of random variables and a limit distribution theorem for a random sum of independent random variables

1966 ◽  
Vol 17 (3-4) ◽  
pp. 401-409 ◽  
Author(s):  
J. Mogyoródi
Keyword(s):  
Limit Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Random Sum ◽  
Distribution Theorem

On a Problem of Fluctuations of Sums of Independent Random Variables

1975 ◽  
Vol 12 (S1) ◽  
pp. 29-37
Author(s):  
Lajos Takács
Keyword(s):  
Limit Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Discrete Random Variables ◽  
Mutually Independent ◽  
Independent And Identically Distributed

The author determines the distribution and the limit distribution of the number of partial sums greater than k (k = 0, 1, 2, …) for n mutually independent and identically distributed discrete random variables taking on the integers 1, 0, − 1, − 2, ….

scholarly journals Limit Distribution of Inventory Level of Perishable Inventory Model

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Hailing Dong ◽  
Guochao Jiang
Keyword(s):  
Explicit Expression ◽  
Limit Distribution ◽  
Random Variables ◽  
Inventory Model ◽  
Independent Random Variables ◽  
General Distribution ◽  
Inventory Level ◽  
Perishable Items ◽  
Perishable Inventory ◽  
Existence Conditions

This paper studies a perishable inventory model, which assumes that each perishable item has finite lifetime, and only one item is consumed each time. The lifetimes of perishable items are independent random variables with the general distribution and so are the consumption internal. Under this assumption, by using backward equations and limit distribution of Markov skeleton processes, this paper obtains the existence conditions and the explicit expression of the limit distribution of the inventory level of perishable inventory model.

scholarly journals On the random functional central limit theorems with almost sure convergence for subsequences

2012 ◽  
Vol 45 (2) ◽  
Author(s):  
Zdzisław Rychlik ◽  
Konrad S. Szuster
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Central Limit Theorems ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Random Sum ◽  
Functional Central Limit Theorems ◽  
Functional Central Limit

AbstractIn this paper we present functional random-sum central limit theorems with almost sure convergence for independent nonidentically distributed random variables. We consider the case where the summation random indices and partial sums are independent. In the past decade several authors have investigated the almost sure functional central limit theorems and related ‘logarithmic’ limit theorems for partial sums of independent random variables. We extend this theory to almost sure versions of the functional random-sum central limit theorems for subsequences.

scholarly journals On trigonometric sums with random frequencies

2018 ◽  
Vol 55 (1) ◽  
pp. 141-152
Author(s):  
Alina Bazarova ◽  
István Berkes ◽  
Marko Raseta
Keyword(s):  
Uniform Distribution ◽  
Lebesgue Measure ◽  
Limit Distribution ◽  
Probability Space ◽  
Random Variables ◽  
Independent Random Variables ◽  
Trigonometric Sums ◽  
Positive Axis ◽  
Positive Integers

We prove that if Ik are disjoint blocks of positive integers and nk are independent random variables on some probability space (Ω,F,P) such that nk is uniformly distributed on Ik, then has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0, 1),B, λ), where B is the Borel σ-algebra and λ is the Lebesgue measure. We also investigate the case when nk have continuous uniform distribution on disjoint intervals Ik on the positive axis.

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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