Related papers: Linear Transformations & the Multivariate Generati…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This…
A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…
We introduce a single generative mechanism with which it is able to describe diverse non-stationary diffusions. A non-stationary Markovian replication process for steps is considered, for which we analytically derive time-evolution of the…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
The n-point statistics of singularity strength variables for multiplicative branching processes is calculated from an analytic expression of the corresponding multivariate generating function. The key ingredient is a branching generating…
Growing dimensionality of data calls for beyond-pairwise interactions quantification. Measures of multidimensional interactions quantification are hindered, among others, by two issues: 1. Interpretation difficulties, 2. the curse of…
We study the connections existing between max-infinitely divisible distributions and Poisson processes from the point of view of functional analysis. More precisely, we derive functional identities for the former by using well-known results…
We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…
In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…
In this paper we study substitutions and some of their associated generating functions. This association takes aperiodicity to transcendence, and vice-versa. These generating functions have a recursive structure arising from the…
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…
The interpretation of coefficients from multivariate linear regression relies on the assumption that the conditional expectation function is linear in the variables. However, in many cases the underlying data generating process is…
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the…
Time series forecasting is crucial for many fields, such as disaster warning, weather prediction, and energy consumption. The Transformer-based models are considered to have revolutionized the field of sequence modeling. However, the…
We survey general properties of multiplicative arithmetic functions of several variables and related convolutions, including the Dirichlet convolution and the unitary convolution. We introduce and investigate a new convolution, called gcd…
The study of the singularities and zeros of the generating functions of multiplicity distributions is advocated. Some hints from well known probability distributions and experimental data are given. The statistical mechanics analogies…
Linear functions of the site frequency spectrum (SFS) play a major role for understanding and investigating genetic diversity. Estimators of the mutation rate (e.g. based on the total number of segregating sites or average of the pairwise…
This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…
In this work we have considered formal power series and partial differential equations, and their relationship with Coding Theory. We have obtained the nature of solutions for the partial differential equations for Cycle Poisson Case. The…