Related papers: Stochastic comparisons of record values based on t…
Memorization in large language models poses critical risks for privacy and fairness as these systems scale to billions of parameters. While previous studies established correlations between memorization and factors like token frequency and…
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 cardinally and ordinally rank distribution functions (CDFs). We present a new class of statistics, maximal adjusted quantiles, and show that a statistic is invariant with respect to cardinal shifts, preserves least upper bounds with…
We characterise probability distributions via a martingale property associated with a natural generalisation of record values, known as $\delta$-records. For an independent and identically distributed sequence $(X_n)$ with running maximum…
We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are…
The (strong) Bruhat order for permutations provides a partial ordering defined as follows: two permutations are comparable if one can be obtained from the other by a sequence of adjacent transpositions that each increase the number of…
Harrel's concordance index is a commonly used discrimination metric for survival models, particularly for models where the relative ordering of the risk of individuals is time-independent, such as the proportional hazards model. There are…
Correlations between planetary and stellar properties, particularly age, can provide insight on planetary formation and evolution processes. However, the underlying source of such trends can be unclear, and measurement uncertainties and…
A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…
Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused…
A way of finding interesting or exceptional records from instant-stamped temporal data is to consider their "durability," or, intuitively speaking, how well they compare with other records that arrived earlier or later, and how long they…
Given two absolutely continuous nonnegative independent random variables, we define the reversed relevation transform as dual to the relevation transform. We first apply such transforms to the lifetimes of the components of parallel and…
It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that…
Widespread population aging has made it critical to understand death rates at old ages. However, studying mortality at old ages is challenging because the data are sparse: numbers of survivors and deaths get smaller and smaller with age. We…
The mid-p-value is a proposed improvement on the ordinary p-value for the case where the test statistic is partially or completely discrete. In this case, the ordinary p-value is conservative, meaning that its null distribution is larger…
Index of proportionality of atomic weights of chemical elements is proposed for determining the relative age of minerals and rocks. Their chemical analysis results serve to be initial data for calculations. For rocks of different…
We introduce new methods of analysing time to event data via extended versions of the proportional hazards and accelerated failure time (AFT) models. In many time to event studies, the time of first observation is arbitrary, in the sense…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
Age is a fundamental stellar property, yet for many stars it is difficult to reliably determine. For M dwarfs it has been notoriously so. Due to their lower masses, core hydrogen fusion proceeds at a much slower rate in M dwarfs than it…
We consider a compositional data analysis approach to forecasting the age distribution of death counts. Using the age-specific period life-table death counts in Australia obtained from the Human Mortality Database, the compositional data…