Towards a theory of negative dependence

2000 ◽  
Vol 41 (3) ◽  
pp. 1371-1390 ◽  
Author(s):  
Robin Pemantle
Keyword(s):  
Negative Dependence

scholarly journals On the distance between convex-ordered random variables, with applications

2002 ◽  
Vol 34 (2) ◽  
pp. 349-374 ◽  
Author(s):  
Michael V. Boutsikas ◽  
Eutichia Vaggelatou
Keyword(s):  
Random Variables ◽  
Simple Approximation ◽  
Negative Dependence ◽  
Exponential Approximation ◽  
Probability Metrics ◽  
Convex Ordering ◽  
Compound Poisson ◽  
Approximation Techniques ◽  
Negatively Dependent Random Variables ◽  
Dependence Concepts

Simple approximation techniques are developed exploiting relationships between generalized convex orders and appropriate probability metrics. In particular, the distance between s-convex ordered random variables is investigated. Results connecting positive or negative dependence concepts and convex ordering are also presented. These results lead to approximations and bounds for the distributions of sums of positively or negatively dependent random variables. Applications and extensions of the main results pertaining to compound Poisson, normal and exponential approximation are provided as well.

scholarly journals Multivariate Eulerian Polynomials and Exclusion Processes

2016 ◽  
Vol 25 (4) ◽  
pp. 486-499 ◽  
Author(s):  
P. BRÄNDÉN ◽  
M. LEANDER ◽  
M. VISONTAI
Keyword(s):  
Finite Number ◽  
Exclusion Process ◽  
Partition Functions ◽  
Asymmetric Exclusion Process ◽  
Negative Dependence ◽  
Combinatorial Interpretation ◽  
Exclusion Processes ◽  
Eulerian Polynomials ◽  
The Third ◽  
Dependence Properties

We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and coloured permutations. The corresponding expressions of the multivariate partition functions are then related to multivariate generalisations of Eulerian polynomials for coloured permutations considered recently by N. Williams and the third author, and others. We also discuss stability and negative dependence properties satisfied by the partition functions.

Examples of Stationary Sequences with Approximate Negative Dependence

2019 ◽  
pp. 305-318
Author(s):  
Florence Merlevède ◽  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Spectral Density ◽  
Point Process ◽  
Point Processes ◽  
Random Variables ◽  
Stationary Processes ◽  
Negative Dependence ◽  
Stationary Sequences ◽  
Determinantal Point Process ◽  
Dependent Random Variables ◽  
Associated Sequences

In this chapter, we treat several examples of stationary processes which are asymptotically negatively dependent and for which the results of Chapter 9 apply. Many systems in nature are complex, consisting of the contributions of several independent components. Our first examples are functions of two independent sequences, one negatively dependent and one interlaced mixing. For instance, the class of asymptotic negatively dependent random variables is used to treat functions of a determinantal point process and a Gaussian process with a positive continuous spectral density. Another example is point processes based on asymptotically negatively or positively associated sequences and displaced according to a Gaussian sequence with a positive continuous spectral density. Other examples include exchangeable processes, the weighted empirical process, and the exchangeable determinantal point process.

scholarly journals Health Care Investment: The Case of Multiple Sources of Risk

2019 ◽  
Vol 27 (2) ◽  
pp. 231-255
Author(s):  
Octave Jokung ◽  
Sovan Mitra
Keyword(s):  
Health Care ◽  
Health Risks ◽  
Policy Implications ◽  
Risk Averse ◽  
Negative Dependence ◽  
Multiple Sources ◽  
Medical Treatments ◽  
Increasing Concave Order ◽  
Increasing Risk ◽  
Demand For Health

Abstract This paper analyses the effect of a bivariate risk on the optimal expenses in health care and gives conditions under which any change in the bivariate risk with respect to the $$\left( {s_{1} ,s_{2} } \right) -$$s1,s2-increasing concave order decreases the expenses in health care. Increasing risk increases the demand for health care for risk-averse and prudent individuals in the multivariate sense. Positive (negative) dependence increases (decreases) expenses in health care. Increasing the correlation produces the same results. Furthermore, the uncertainty surrounding the effectiveness of medical treatments amplifies the effect of any change in wealth and health risks. We also present some policy implications.

scholarly journals On Minimal Copulas under the Concordance Order

2019 ◽  
Vol 184 (3) ◽  
pp. 762-780 ◽  
Author(s):  
Jae Youn Ahn ◽  
Sebastian Fuchs
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Negative Dependence ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Minimal Elements ◽  
Measures Of Concordance ◽  
Concordance Order

AbstractIn the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $$d\ge 3$$d≥3, the set of all minimal elements in the collection of all copulas turns out to be a natural and quite important extreme negative dependence concept. We investigate several sufficient conditions, and we provide a necessary condition for a copula to be minimal. The sufficient conditions are related to the extreme negative dependence concept of d-countermonotonicity and the necessary condition is related to the collection of all copulas minimizing multivariate Kendall’s tau. The concept of minimal copulas has already been proved to be useful in various continuous and concordance order preserving optimization problems including variance minimization and the detection of lower bounds for certain measures of concordance. We substantiate this key role of minimal copulas by showing that every continuous and concordance order preserving functional on copulas is minimized by some minimal copula, and, in the case the continuous functional is even strictly concordance order preserving, it is minimized by minimal copulas only. Applying the above results, we may conclude that every minimizer of Spearman’s rho is also a minimizer of Kendall’s tau.

scholarly journals A Sarmanov Distribution with Beta Marginals: An Application to Motor Insurance Pricing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2020
Author(s):  
Catalina Bolancé ◽  
Montserrat Guillen ◽  
Albert Pitarque
Keyword(s):  
Beta Distribution ◽  
Relative Frequency ◽  
Linear Models ◽  
Speed Limit ◽  
Negative Dependence ◽  
Night Time ◽  
Generalised Linear Models ◽  
Insurance Pricing ◽  
High Quantiles ◽  
Motor Insurance

Background: The Beta distribution is useful for fitting variables that measure a probability or a relative frequency. Methods: We propose a Sarmanov distribution with Beta marginals specified as generalised linear models. We analyse its theoretical properties and its dependence limits. Results: We use a real motor insurance sample of drivers and analyse the percentage of kilometres driven above the posted speed limit and the percentage of kilometres driven at night, together with some additional covariates. We fit a Beta model for the marginals of the bivariate Sarmanov distribution. Conclusions: We find negative dependence in the high quantiles indicating that excess speed and night-time driving are not uniformly correlated.

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