Finding the principal points of a random variable

Emilio Carrizosa; E. Conde; A. Castaño; D. Romero-Morales

Displaying similar documents to “Finding the principal points of a random variable”

On the optimal setting of the $h p$ -version of the finite element method

Chleboun, Jan

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The goal of this contribution is to find the optimal finite element space for solving a particular boundary value problem in one spatial dimension. In other words, the optimal use of available degrees of freedom is sought after. This is done through optimizing both the mesh and the polynomial degree of the basis functions. The resulting combinatorial optimization problem is solved in parallel by a Matlab program running on a cluster of multi-core personal computers.

Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

Jonathon Peterson, Gennady Samorodnitsky (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter $κ g t; 0$ that determines the fluctuations of the process. When $0 l t; κ l t; 2$ , the averaged distributions of the hitting times of the random walk converge to a $κ$ -stable distribution. However, it was shown recently that in this case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true...

Characterizations of continuous distributions through inequalities involving the expected values of selected functions

Faranak Goodarzi, Mohammad Amini, Gholam Reza Mohtashami Borzadaran (2017)

Applications of Mathematics

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Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser’s function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via $w (\cdot)$ -function defined by Cacoullos...

Premium evaluation for different loss distributions using utility theory

Harman Preet Singh Kapoor, Kanchan Jain (2011)

Discussiones Mathematicae Probability and Statistics

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For any insurance contract to be mutually advantageous to the insurer and the insured, premium setting is an important task for an actuary. The maximum premium ( $P_{m a x})$ that an insured is willing to pay can be determined using utility theory. The main focus of this paper is to determine $P_{m a x}$ by considering different forms of the utility function. The loss random variable is assumed to follow different Statistical distributions viz Gamma, Beta, Exponential, Pareto, Weibull, Lognormal and Burr....

An optimal matching problem

Ivar Ekeland (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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Given two measured spaces $(X, μ)$ and $(Y, ν)$ , and a third space $Z$ , given two functions $u (x, z)$ and $v (x, z)$ , we study the problem of finding two maps $s : X \to Z$ and $t : Y \to Z$ such that the images $s (μ)$ and $t (ν)$ coincide, and the integral $\int_{X} u (x, s (x)) d μ - \int_{Y} v (y, t (y)) d ν$ is maximal. We give condition on $u$ and $v$ for which there is a unique solution.

Finite canonization

Saharon Shelah (1996)

Commentationes Mathematicae Universitatis Carolinae

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The canonization theorem says that for given $m, n$ for some $m^{*}$ (the first one is called $E R (n; m)$ ) we have for every function $f$ with domain ${[1, \dots, m^{*}]}^{n}$ , for some $A \in {[1, \dots, m^{*}]}^{m}$ , the question of when the equality $f (i_{1}, \dots, i_{n}) = f (j_{1}, \dots, j_{n})$ (where $i_{1} < \dots < i_{n}$ and $j_{1} < \dots j_{n}$ are from $A$ ) holds has the simplest answer: for some $v \subseteq {1, \dots, n}$ the equality holds iff $⋀_{ℓ \in v} i_{ℓ} = j_{ℓ}$ . We improve the bound on $E R (n, m)$ so that fixing $n$ the number of exponentiation needed to calculate $E R (n, m)$ is best possible.

Geometrically strictly semistable laws as the limit laws

Marek T. Malinowski (2007)

Discussiones Mathematicae Probability and Statistics

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A random variable X is geometrically infinitely divisible iff for every p ∈ (0,1) there exists random variable $X_{p}$ such that $X \overset{d}{=} \sum_{k = 1}^{T (p)} X_{p, k}$ , where $X_{p, k}$ ’s are i.i.d. copies of $X_{p}$ , and random variable T(p) independent of $X_{p, 1}, X_{p, 2}, . . .$ has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The main results concern geometrically strictly semistable distributions which form a subset of geometrically infinitely divisible distributions....

Distributed dual averaging algorithm for multi-agent optimization with coupled constraints

Zhipeng Tu, Shu Liang (2024)

Kybernetika

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This paper investigates a distributed algorithm for the multi-agent constrained optimization problem, which is to minimize a global objective function formed by a sum of local convex (possibly nonsmooth) functions under both coupled inequality and affine equality constraints. By introducing auxiliary variables, we decouple the constraints and transform the multi-agent optimization problem into a variational inequality problem with a set-valued monotone mapping. We propose a distributed...

Comparison of order statistics in a random sequence to the same statistics with I.I.D. variables

Jean-Louis Bon, Eugen Păltănea (2006)

ESAIM: Probability and Statistics

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The paper is motivated by the stochastic comparison of the reliability of non-repairable $k$ -out-of- $n$ systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let $U_{i}, i = 1, . . ., n,$ be positive independent random variables with common distribution $F$ . For $λ_{i} > 0$ and $μ > 0$ , let consider $X_{i} = U_{i} / λ_{i}$ and $Y_{i} = U_{i} / μ, i = 1, . . ., n$ . Remark that this is no more than a change of scale for each term. For $k \in {1, 2, . . ., n},$ let us define $X_{k : n}$ to be the $k$ th order...