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We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation…
In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent…
In this paper we analyze the effects of stochastic resetting on an encounter-based model of an unbiased run-and-tumble particle (RTP) confined to the half-line $[0,\infty)$ with a partially absorbing wall at $x=0$. The RTP tumbles at a…
Statistical modeling of physical laws connects experiments with mathematical descriptions of natural phenomena. The modeling is based on the probability density of measured variables expressed by experimental data via a kernel estimator. As…
Degradation data are considered for assessing reliability in highly reliable systems. The usual assumption is that degradation units come from a homogeneous population. But in presence of high variability in the manufacturing process, this…
We study the continuity property of the generalized entropy as a function of the underlying probability distribution, defined with an action space and a loss function, and use this property to answer the basic questions in statistical…
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…
In the recent information-theoretic literature, the concept of extropy has been studied for order statistics. In the present communication we consider a cumulative analogue of extropy in the same vein of cumulative residual (past) entropy…
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
A new lifetime model, named the Modi linear failure rate distribution, is suggested. This flexible model is capable of accommodating a wide range of hazard rate shapes, including decreasing, increasing, bathtub, upside-down bathtub, and…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
A one-dimensional run-and-tumble particle (RTP) switches randomly between a left and right moving state of constant speed $v$. This type of motion arises in a wide range of applications in cell biology, including the unbiased growth and…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Accurately estimating the remaining useful life (RUL) of industrial machinery is beneficial in many real-world applications. Estimation techniques have mainly utilized linear models or neural network based approaches with a focus on short…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
Survival analysis provides a well-established framework for modeling time-to-event data, with hazard and survival functions formally defined as population-level quantities. In applied work, however, these quantities are often interpreted as…
This paper introduces and studies a new uncertainty measure, the cumulative residual interval entropy (CRIE). Defined as the cumulative residual entropy of a doubly truncated (interval) continuous random variable, this measure has several…
Partially observed stochastic systems can appear (almost) time-reversal symmetric while in fact operating far from equilibrium. The present work extends the perturbative framework introduced in [Phys. Rev. Lett. 136, 198302 (2026)] to…
We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…
An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting…