On sufficient conditions for the comparison in the excess wealth order and spacings

2016 ◽  
Vol 53 (1) ◽  
pp. 33-46 ◽  
Author(s):  
Félix Belzunce ◽  
Carolina Martínez-Riquelme ◽  
José M. Ruiz ◽  
Miguel A. Sordo
Keyword(s):  
Order Statistics ◽  
Sufficient Conditions ◽  
The Other ◽  
Generalized Order Statistics ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Dispersive Order ◽  
Excess Wealth Order ◽  
The One ◽  
Quantities Of Interest

Abstract The purpose of this paper is twofold. On the one hand, we provide sufficient conditions for the excess wealth order. These conditions are based on properties of the quantile functions which are useful when the dispersive order does not hold. On the other hand, we study sufficient conditions for the comparison in the increasing convex order of spacings of generalized order statistics. These results will be combined to show how we can provide comparisons of quantities of interest in reliability and insurance.

scholarly journals On the Increasing Convex Order of Relative Spacings of Order Statistics

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 618
Author(s):  
Antonia Castaño-Martínez ◽  
Gema Pigueiras ◽  
Miguel A. Sordo
Keyword(s):  
Order Statistics ◽  
Relative Deprivation ◽  
Sufficient Conditions ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Income Distributions ◽  
Parametric Families ◽  
Relative Differences

Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex order of relative spacings of two distributions from the case of consecutive spacings to general spacings. The sufficient conditions are given in terms of the expected proportional shortfall order. As an application, we compare relative deprivation within some parametric families of income distributions.

scholarly journals On strict sub-Gaussianity, optimal proxy variance and symmetry for bounded random variables

2020 ◽  
Vol 24 ◽  
pp. 39-55
Author(s):  
Julyan Arbel ◽  
Olivier Marchal ◽  
Hien D. Nguyen
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Random Variables ◽  
The Other ◽  
Bounded Support ◽  
Uniform Distributions ◽  
Standard Variance ◽  
Per Se ◽  
The One ◽  
The Relationship

We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these questions is how to characterize the optimal sub-Gaussian proxy variance? Another question is how to characterize strict sub-Gaussianity, defined by a proxy variance equal to the (standard) variance? We address the questions in proposing conditions based on the study of functions variations. A particular focus is given to the relationship between strict sub-Gaussianity and symmetry of the distribution. In particular, we demonstrate that symmetry is neither sufficient nor necessary for strict sub-Gaussianity. In contrast, simple necessary conditions on the one hand, and simple sufficient conditions on the other hand, for strict sub-Gaussianity are provided. These results are illustrated via various applications to a number of bounded random variables, including Bernoulli, beta, binomial, Kumaraswamy, triangular, and uniform distributions.

Stochastic comparisons of interfailure times under a relevation replacement policy

2017 ◽  
Vol 54 (1) ◽  
pp. 134-145 ◽  
Author(s):  
Miguel A. Sordo ◽  
Georgios Psarrakos
Keyword(s):  
Stochastic Order ◽  
Replacement Policy ◽  
Convex Order ◽  
Stochastic Comparisons ◽  
Increasing Convex Order ◽  
Failure Times ◽  
Usual Stochastic Order ◽  
Comparison Results ◽  
Excess Wealth Order ◽  
Cumulative Residual

AbstractWe provide some results for the comparison of the failure times and interfailure times of two systems based on a replacement policy proposed by Kapodistria and Psarrakos (2012). In particular, we show that when the first failure times are ordered in terms of the dispersive order (or, the excess wealth order), then the successive interfailure times are ordered in terms of the usual stochastic order (respectively, the increasing convex order). As a consequence, we provide comparison results for the cumulative residual entropies of the systems and their dynamic versions.

scholarly journals ON HYBRID SEQUENCES BUILT FROM NIEDERREITER–HALTON SEQUENCES AND KRONECKER SEQUENCES

2011 ◽  
Vol 84 (2) ◽  
pp. 238-254 ◽  
Author(s):  
ROSWITHA HOFER ◽  
PETER KRITZER
Keyword(s):  
Uniform Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Future Research ◽  
Short Summary ◽  
The One ◽  
Halton Sequences ◽  
Necessary And Sufficient

AbstractWe discuss the distribution properties of hybrid sequences whose components stem from Niederreiter–Halton sequences on the one hand, and Kronecker sequences on the other. In this paper, we give necessary and sufficient conditions on the uniform distribution of such sequences, and derive a result regarding their discrepancy. We conclude with a short summary and a discussion of topics for future research.

Answerability

2018 ◽  
Author(s):  
Natalie Stoljar
Keyword(s):  
Moral Responsibility ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Alternative Approach ◽  
The One ◽  
Necessary And Sufficient

This chapter defends externalist or “constitutively relational” conceptions of autonomy through an examination of an alternative approach developed by Andrea Westlund. Westlund develops her approach in response to what has been called the “agency dilemma.” On the one hand, constraining external circumstances seem to undermine autonomy; on the other, the claim that people are nonautonomous because of their circumstances seems to erase their agency and disrespect their evaluative commitments. This chapter distinguishes the necessary and sufficient conditions of several interrelated aspects of agency: autonomy, authentic agential perspective, and moral responsibility. I argue that whereas answerability may be sufficient for moral responsibility, it is not sufficient for autonomy. Objections to externalist conceptions of autonomy, including the agency dilemma, wrongly assume that denying autonomy implies erasing agency. Once it is recognized that autonomy does not always overlap with authentic agential perspective or moral responsibility, the objections lose their force.

Increasing convex order on generalized aggregation of SAI random variables with applications

2017 ◽  
Vol 54 (3) ◽  
pp. 685-700 ◽  
Author(s):  
Xiaoqing Pan ◽  
Xiaohu Li
Keyword(s):  
Linear Combination ◽  
Kernel Function ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Special Cases ◽  
Arrangement Increasing

Abstract In this paper we study general aggregation of stochastic arrangement increasing random variables, including both the generalized linear combination and the standard aggregation as special cases. In terms of monotonicity, supermodularity, and convexity of the kernel function, we develop several sufficient conditions for the increasing convex order on the generalized aggregations. Some applications in reliability and risks are also presented.

scholarly journals Stochastic orders and majorization of mean order statistics

2006 ◽  
Vol 43 (03) ◽  
pp. 704-712 ◽  
Author(s):  
Jesús de la Cal ◽  
Javier Cárcamo
Keyword(s):  
Order Statistics ◽  
Random Variables ◽  
Stochastic Orders ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Finite Dimensional ◽  
Integrable Functions

We characterize the (continuous) majorization of integrable functions introduced by Hardy, Littlewood, and Pólya in terms of the (discrete) majorization of finite-dimensional vectors, introduced by the same authors. The most interesting version of this result is the characterization of the (increasing) convex order for integrable random variables in terms of majorization of vectors of expected order statistics. Such a result includes, as particular cases, previous results by Barlow and Proschan and by Alzaid and Proschan, and, in a sense, completes the picture of known results on order statistics. Applications to other stochastic orders are also briefly considered.

scholarly journals Joint desirability foundations of social choice and opinion pooling

2021 ◽  
Author(s):  
Arianna Casanova ◽  
Enrique Miranda ◽  
Marco Zaffalon
Keyword(s):  
Social Choice ◽  
Sufficient Conditions ◽  
The Other ◽  
Incomplete Preferences ◽  
Inherent Limitation ◽  
Uncertainty Model ◽  
The Status ◽  
Opinion Pooling ◽  
New Perspective ◽  
The One

AbstractWe develop joint foundations for the fields of social choice and opinion pooling using coherent sets of desirable gambles, a general uncertainty model that allows to encompass both complete and incomplete preferences. This leads on the one hand to a new perspective of traditional results of social choice (in particular Arrow’s theorem as well as sufficient conditions for the existence of an oligarchy and democracy) and on the other hand to using the same framework to analyse opinion pooling. In particular, we argue that weak Pareto (unanimity) should be given the status of a rationality requirement and use this to discuss the aggregation of experts’ opinions based on probability and (state-independent) utility, showing some inherent limitation of this framework, with implications for statistics. The connection between our results and earlier work in the literature is also discussed.

scholarly journals Dispersive order comparisons on extreme order statistics from homogeneous dependent random vectors

2021 ◽  
Vol 9 (1) ◽  
pp. 385-393
Author(s):  
Mhamed Mesfioui ◽  
Julien Trufin
Keyword(s):  
Order Statistics ◽  
Sufficient Conditions ◽  
Random Vectors ◽  
Dispersive Order ◽  
Extreme Order Statistics ◽  
Preservation Property

Abstract In this paper, we investigate sufficient conditions for preservation property of the dispersive order for the smallest and largest order statistics of homogeneous dependent random vectors. Moreover, we establish sufficient conditions for ordering with the dispersive order the largest order statistics from dependent homogeneous samples of different sizes.

scholarly journals On the Global Dissipativity of a Class of Cellular Neural Networks with Multipantograph Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Liqun Zhou
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Variable Coefficients ◽  
The Other ◽  
Algebraic Methods ◽  
Lyapunov Functionals ◽  
The One ◽  
Delay Dependent ◽  
First Time

For the first time the global dissipativity of a class of cellular neural networks with multipantograph delays is studied. On the one hand, some delay-dependent sufficient conditions are obtained by directly constructing suitable Lyapunov functionals; on the other hand, firstly the transformation transforms the cellular neural networks with multipantograph delays into the cellular neural networks with constant delays and variable coefficients, and then constructing Lyapunov functionals, some delay-independent sufficient conditions are given. These new sufficient conditions can ensure global dissipativity together with their sets of attraction and can be applied to design global dissipative cellular neural networks with multipantograph delays and easily checked in practice by simple algebraic methods. An example is given to illustrate the correctness of the results.

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