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The probability of the survival of the population of individuals of both sexes of given mature age, procreation rate and structure stability has been searched in the numerical experiment. The populations with long period of reproduction and…
We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed…
We consider a small set of axioms for income averaging -- recursivity, continuity, and the boundary condition for the present. These properties yield a unique averaging function that is the density of the reflected Brownian motion with a…
We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…
Regression models are essential for a wide range of real-world applications. However, in practice, target values are not always precisely known; instead, they may be represented as intervals of acceptable values. This challenge has led to…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
In usual demographic analysis, force of mortality is a function of one variable, that is, of age. In this article bi-variate and multivariate force of mortality functions are introduced for the first time to explain mortality differentials.…
We consider dynamic versions of the mutual information of lifetime distributions, with focus on past lifetimes, residual lifetimes and mixed lifetimes evaluated at different instants. This allows to study multicomponent systems, by…
Educational policymakers often lack data on student outcomes where standardized tests were not administered. Machine learning can predict unobserved outcomes in target populations using source population data. However, covariate…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Human mobility forms the backbone of contact patterns through which infectious diseases propagate, fundamentally shaping the spatio-temporal dynamics of epidemics and pandemics. While traditional models are often based on the assumption…
The promise of equal opportunity is a cornerstone of modern societies, yet upward economic mobility remains out of reach for many. Using a decade of population-scale social network data from the Netherlands, covering over a billion family,…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
Some partial orderings which compare probability distributions with the expo- nential distribution, are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which de-…
We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…
A toy statistical model which mimics localized-to-itinerant electron transitions is introduced. We consider a system of two types of charge carriers: (1) localized ones, and (2) itinerant ones. There is chemical equilibrium between these…
We prove the $L^{2}$ convergence for the linear multiple ergodic averages of commuting transformations $T_{1}, ..., T_{l}$, assuming that each map $T_i$ and each pair $T_iT_j^{-1}$ is ergodic for $i\neq j$. The limiting behavior of such…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
We introduce a two-parameter modification of the cofinality invariant of ideals. This allows us to include the interaction of a pair of ideals in the study of base-like structures. We find the values (cardinal numbers or well-known cardinal…