Related papers: The Bivariate Lack-of-Memory Distributions

The problem of estimating location (scale) parameters $\theta_1$ and $\theta_2$ of two distributions when the ordering between them is known apriori (say, $\theta_1\leq \theta_2$) has been extensively studied in the literature. Many of…

In this article we suggest a new statistical approach considering survival heterogeneity as a breakpoint model in an ordered sequence of time to event variables. The survival responses need to be ordered according to a numerical covariate.…

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only…

In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…

Statistical inference based on moment conditions and estimating equations is of substantial interest when it is difficult to specify a full probabilistic model. We propose a Bayesian flavored model selection framework based on…

In this paper, we proposed a new lifetime distribution namely generalized weighted Lindley (GLW) distribution. The GLW distribution is a useful generalization of the weighted Lindley distribution, which accommodates increasing, decreasing,…

We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…

We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…

Regression models have a substantial impact on interpretation of treatments, genetic characteristics and other potential risk factors in survival analysis. In many applications, the description of censoring and survival curve reveals the…

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…

Preference learning (PL) with large language models (LLMs) aims to align the LLMs' generations with human preferences. Previous work on reinforcement learning from human feedback (RLHF) has demonstrated promising results in in-distribution…

To address the needs of modeling uncertainty in sensitive machine learning applications, the setup of distributionally robust optimization (DRO) seeks good performance uniformly across a variety of tasks. The recent multi-distribution…

Applications of machine learning (ML) techniques to operational settings often face two challenges: i) ML methods mostly provide point predictions whereas many operational problems require distributional information; and ii) They typically…

A central challenge in continual learning is forgetting, the loss of performance on previously learned tasks induced by sequential adaptation to new ones. While forgetting has been extensively studied empirically, rigorous theoretical…

We study a fundamental class of regression models called the second order linear model (SLM). The SLM extends the linear model to high order functional space and has attracted considerable research interest recently. Yet how to efficiently…

A time-varying bivariate copula joint model, which models the repeatedly measured longitudinal outcome at each time point and the survival data jointly by both the random effects and time-varying bivariate copulas, is proposed in this…

The Luria-Delbr\"uck distribution is a classical model of mutations in cell kinetics. It is obtained as a limit when the probability of mutation tends to zero and the number of divisions to infinity. It can be interpreted as a compound…

A persistent paradox in continual learning (CL) is that neural networks often retain linearly separable representations of past tasks even when their output predictions fail. We formalize this distinction as the gap between deep…

In this paper, we propose a log-symmetric survival model with cure fraction, considering that the distributions of lifetimes for susceptible individuals belong to the log-symmetric class of distributions. This class has continuous, strictly…

There is no easy extension of Kaplan-Meier and Nelson-Aalen estimators to the bivariate case, and estimating bivariate survival distributions nonparametrically is associated with various non-trivial problems. The Dabrowska estimator will…