Related papers: Geometric and Harmonic Aging Intensity function an…
The reversed aging intensity function is defined as the ratio of the instantaneous reversed hazard rate to the baseline value of the reversed hazard rate. It analyzes the aging property quantitatively, the higher the reversed aging…
The ageing intensity function is a powerful analytical tool that provides valuable insights into the ageing process across diverse domains such as reliability engineering, actuarial science, and healthcare. Its applications continue to…
The relative ageing is an important notion which is useful to measure how a system ages relative to another one. Among all existing stochastic orders, there are two important orders describing the relative ageing of two systems, namely,…
This paper introduces a simple index that helps to assess the degree of aging or rejuvenation of a (non)repairable system. The index ranges from -1 to 1 and is negative for the class of decreasing failure rate distributions (or…
Aging phenomena are examples of `non-equilibrium criticality' and can be exemplified by systems with Galilean and scaling symmetries but no time translation invariance. We realize aging holographically using a deformation of a…
Relative ageing describes how a system ages with respect to another one. The ageing faster orders are the ones which compare the relative ageings of two systems. Here, we study ageing faster orders in the hazard and the reversed hazard…
Aging, as defined in terms of the slope of the probability of death versus time (hazard curve), is a generic phenomenon observed in nearly all complex systems. Theoretical models of aging predict hazard curves that monotonically increase in…
We introduce some new generalized stochastic orderings (in the spirit of relative ageing) which compare probability distributions with the exponential distribution. These orderings are useful to understand the phenomenon of positive ageing…
Recently, authors have studied inequalities involving expectations of selected functions viz. failure rate, mean residual life, aging intensity function and log-odds rate which are defined for left truncated random variables in reliability…
Aging is a multidimensional process where phenotypes change at varying rates. Longitudinal studies of aging typically involve following a cohort of individuals over the course of several years. This design is hindered by cost, attrition,…
Although proportional hazard rate model is a very popular model to analyze failure time data, sometimes it becomes important to study the additive hazard rate model. Again, sometimes the concept of the hazard rate function is abstract, in…
We review the most striking experimental results on aging in a variety of disordered systems, which reveal similar features but also important differences. We argue that a generic model that reproduce many of these features is that of {\it…
In this paper we investigate the flexibility of matrix distributions for the modeling of mortality. Starting from a simple Gompertz law, we show how the introduction of matrix-valued parameters via inhomogeneous phase-type distributions can…
New models for evolutionary processes of mutation accumulation allow hypotheses about the age-specificity of mutational effects to be translated into predictions of heterogeneous population hazard functions. We apply these models to…
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…
Suppose that a target function is monotonic, namely, weakly increasing, and an available original estimate of this target function is not weakly increasing. Rearrangements, univariate and multivariate, transform the original estimate to a…
The low temperature Monte Carlo dynamics of an ensemble of linear harmonic oscillators shows some entropic barriers related to the difficulty of finding the directions in configurational space which decrease the energy. This mechanism is…
We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a…
Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real L{\'e}vy process. This gives a simple and unified proof of several results in the literature,…
In epidemiological or demographic studies, with variable age at onset, a typical quantity of interest is the incidence of a disease (for example the cancer incidence). In these studies, the individuals are usually highly heterogeneous in…