Related papers: Conflations of Probability Distributions
We consider $N$ events that are defined on a common probability space. Those events shell have a common probability function that is symmetric with respect to interchanging the events. We ask for the probability distribution of the number…
A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a…
We introduce a quantum generalisation of the notion of coupling in probability theory. Several interesting examples and basic properties of quantum couplings are presented. In particular, we prove a quantum extension of Strassen theorem for…
Predictive distributions need to be aggregated when probabilistic forecasts are merged, or when expert opinions expressed in terms of probability distributions are fused. We take a prediction space approach that applies to discrete, mixed…
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint,…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences…
In the present paper a generalization of Gurland distribution [3] is obtained as a beta mixture of the generalized Poisson distribution (GPD) of Consul and Jain [2]. The first two moments of the distribution and a recurrence relation among…
We formulate an info-clustering paradigm based on a multivariate information measure, called multivariate mutual information, that naturally extends Shannon's mutual information between two random variables to the multivariate case…
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.…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into…
Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…
Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are independent realizations of random variables X and Z respectively, where we further believe that Z=X+Y with Y independent of X, the problem is to estimate the distribution…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
The commuting probability of a finite group is defined to be the probability that two randomly chosen group elements commute. Let P \subset (0,1] be the set of commuting probabilities of all finite groups. We prove that every point of P is…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…