Related papers: Marginality in non-compatible random events
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
Stochastic large scale interacting systems can be studied via the observables, i.e. functions on the underlying configuration space. In our previous article, we introduced the concept of uniform functions, which are suitable class of…
A new multiplicity distribution with multifractal properties which can be used in high-energy physics and quantum optics is proposed. It may be considered as a generalization of the negative-binomial distribution. We find the structure of…
Nontransitive choices have long been an area of curiosity within economics. However, determining whether nontransitive choices represent an individual's preference is a difficult task since choice data is inherently stochastic. This paper…
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. A special inequality which…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
A marginal problem asks whether a given family of marginal distributions for some set of random variables arises from some joint distribution of these variables. Here we point out that the existence of such a joint distribution imposes…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of…
We know that the marginals in a multinomial distribution are binomial variates exhibiting a negative correlation. But we can construct two linear combinations of such marginals in such a way to obtain a positive correlation. We discuss the…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…
In this note, we analyze joint probability distributions that arise from outcomes of sequences of quantum measurements performed on sets of quantum states. First, we identify some properties of these distributions that need to be fulfilled…
This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
We consider a semiparametric generalized linear model and study estimation of both marginal and quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic…
In a regression analysis, suppose we suspect that there are several heterogeneous groups in the population that a sample represents. Mixture regression models have been applied to address such problems. By modeling the conditional…