Related papers: Ordered Probabilistic Choice
A factor copula model is proposed in which factors are either simulable or estimable from exogenous information. Point estimation and inference are based on a simulated methods of moments (SMM) approach with non-overlapping simulation…
Rank-based dependence measures such as Spearman's footrule are robust and invariant, but they often fail to capture directional or asymmetric dependence in multivariate settings. This paper introduces a new family of directional Spearman's…
The Multiplicative Error Model (Engle (2002)) for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
In many practical situations, we know the probabilities $a$ and $b$ of two events $A$ and $B$, and we want to estimate the joint probability ${\rm Prob}(A\,\&\,B)$. The algorithm that estimates the joint probability based on the known…
Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and…
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences…
Under a mild condition we give closed-form expressions for copulas of systems that consist of maxima and of minima of subvectors of a given random vector $X$ with continuous marginals. Said expressions appear explicit in the copula of $X$…
This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of $Phi$-divergences. An axiomatic framework for this purpose is provided, after which we…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the `right' copula is not an easy task, and the…
We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central notion is that of all possible couplings for…
Functional dependencies restrict the potential interactions among variables connected in a probabilistic network. This restriction can be exploited in qualitative probabilistic reasoning by introducing deterministic variables and modifying…
An extension of Archimax copula class in more than two random variables ( Multivariate ) was introduced in (J\'agr 2011) for describing dependency structures among random variables in higher dimension, and some properties of Archimax copula…
Copulas are now frequently used to construct or estimate multivariate distributions because of their ability to take into account the multivariate dependence of the different variables while separately specifying marginal distributions.…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
Many types of bounded data defined on the unit interval arise naturally as ratios of the form $X/(X + Y)$. In the existing literature, the main statistical models proposed for this type of bounded data typically based on the assumption that…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…
Estimating dependence relationships between variables is a crucial issue in many applied domains, such as medicine, social sciences and psychology. When several variables are entertained, these can be organized into a network which encodes…
When scholars study joint distributions of multiple variables, copulas are useful. However, if the variables are not linearly correlated with each other yet are still not independent, most of conventional copulas are not up to the task.…