scholarly journals Distribution functions of linear combinations of lattice polynomials from the uniform distribution

2008 ◽  
Vol 78 (8) ◽  
pp. 985-991 ◽  
Author(s):  
Jean-Luc Marichal ◽  
Ivan Kojadinovic
Keyword(s):  
Uniform Distribution ◽  
Distribution Functions ◽  
Linear Combinations ◽  
Lattice Polynomials

A geometric interpretation of the relations between the exponential and generalized Erlang distributions

1982 ◽  
Vol 14 (04) ◽  
pp. 885-897 ◽  
Author(s):  
Michel Dehon ◽  
Guy Latouche
Keyword(s):  
Vector Space ◽  
Convex Subset ◽  
Geometric Interpretation ◽  
Distribution Functions ◽  
Real Vector ◽  
Exponential Distributions ◽  
Geometric Aspect ◽  
Linear Combinations ◽  
Exponential Random Variables ◽  
Erlang Distributions

Linear combinations of exponential distribution functions are considered, and the class of distribution functions so obtainable is investigated. Convex combinations correspond to hyperexponential distributions, while non-convex combinations yield, among other, generalized Erlang distributions obtainable as sums of independent exponential random variables with different parameters. For a given number n of different exponential distributions, the class investigated is an (n – 1)-dimensional convex subset of the n-dimensional real vector space generated by the n distribution functions. The geometric aspect of this subset is revealed, together with the location of hyperexponential and generalized Erlang distributions.

On the Overall Properties of Composites Reinforced by Fibers With Prescribed Orientations

2015 ◽  
Author(s):  
Yana Morenko ◽  
Pavlo Krokhmal ◽  
Olesya I. Zhupanska
Keyword(s):  
Uniform Distribution ◽  
Elastic Properties ◽  
Optimization Problem ◽  
Distribution Functions ◽  
Fiber Reinforced Composites ◽  
Semidefinite Optimization ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Positive Semidefinite Matrices ◽  
Orientational Distribution

This study is concerned with development of bounds on the elastic properties of fiber reinforced composites with arbitrary orientational distribution of fibers. Generalization of the Mori-Tanaka model [1] and Hashin-Schtrikman variational bounds [2] to the cases of non-aligned composite phases are examined. Orientation distribution functions (ODF) are used to describe orientation probability density. It is shown that the Mori-Tanaka scheme applied to the non-aligned fiber reinforced composites violates symmetry of the effective elastic moduli tensor. The study of the literature also reveals that there are no known bounds derived for the composites with orientational distribution (except for the random uniform distribution) of phases. To overcome this issue we propose to formulate a problem of finding tightest bounds for the composites with non-aligned phases as a nonlinear semidefinite optimization problem, i.e., an optimization problem where the optimization variables are represented by symmetric positive semidefinite matrices. Such a formulation guarantees that any solution of the optimization problem represents a valid tensor of elastic material properties. The optimization problem then is solved by an interior point method to produce optimal bounds for the overall elastic properties of two-phase composite with uniform distribution of carbon nanotubes in a polymer matrix.

scholarly journals Distribution functions of ratio sequences. An expository paper

2015 ◽  
Vol 64 (1) ◽  
pp. 133-185
Author(s):  
Oto Strauch
Keyword(s):  
Uniform Distribution ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
One Step ◽  
Expository Paper ◽  
Positive Integers

Abstract This expository paper presents known results on distribution functions g(x) of the sequence of blocks where xn is an increasing sequence of positive integers. Also presents results of the set G(Xn) of all distribution functions g(x). Specially: - continuity of g(x); - connectivity of G(Xn); - singleton of G(Xn); - one-step g(x); - uniform distribution of Xn, n = 1, 2, . . . ; - lower and upper bounds of g(x); - applications to bounds of ; - many examples, e.g., , where pn is the nth prime, is uniformly distributed. The present results have been published by 25 papers of several authors between 2001-2013.

Convergence rate of perturbed empirical distribution functions

1979 ◽  
Vol 16 (01) ◽  
pp. 163-173 ◽  
Author(s):  
B. B. Winter
Keyword(s):  
Distribution Function ◽  
Convergence Rate ◽  
Uniform Distribution ◽  
Empirical Distribution ◽  
Distribution Functions ◽  
Unit Mass ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Empirical Distribution Functions ◽  
Non Parametric

Given an i.i.d. sequenceX1,X2, … with common distribution function (d.f.) F, the usual non-parametric estimator ofFis the e.d.f.Fn;whereUois the d.f. of the unit mass at zero. Anadmissible perturbation of the e.d.f., say, is obtained ifUois replaced by a d.f., whereis a sequence of d.f.'s converging weakly toUo.Suchperturbed e.d.f.′s arise quite naturally as integrals of non-parametric density estimators, e.g. as. It is shown that if F satisfies some smoothness conditions and the perturbation is not too drastic then‘has the Chung–Smirnov property'; i.e., with probability one,1. But if the perturbation is too vigorous then this property is lost: e.g., if F is the uniform distribution andHnis the d.f. of the unit mass atn–αthen the above lim sup is ≦ 1 or = ∞, depending on whetheror

A geometric interpretation of the relations between the exponential and generalized Erlang distributions

1982 ◽  
Vol 14 (4) ◽  
pp. 885-897 ◽  
Author(s):  
Michel Dehon ◽  
Guy Latouche
Keyword(s):  
Vector Space ◽  
Convex Subset ◽  
Geometric Interpretation ◽  
Distribution Functions ◽  
Real Vector ◽  
Exponential Distributions ◽  
Geometric Aspect ◽  
Linear Combinations ◽  
Exponential Random Variables ◽  
Erlang Distributions

Linear combinations of exponential distribution functions are considered, and the class of distribution functions so obtainable is investigated. Convex combinations correspond to hyperexponential distributions, while non-convex combinations yield, among other, generalized Erlang distributions obtainable as sums of independent exponential random variables with different parameters.For a given number n of different exponential distributions, the class investigated is an (n – 1)-dimensional convex subset of the n-dimensional real vector space generated by the n distribution functions. The geometric aspect of this subset is revealed, together with the location of hyperexponential and generalized Erlang distributions.

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