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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning 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for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models Direct Estimation of Schrödinger Bridge Time-Series Drifts: Finite-Sample, Asymptotic, and Adaptive Guarantees Information-theoretic Limits of Learning and Estimation Adaptivity Under Realizability Constraints: Comparing In-Context and Agentic Learning Multiscale Euclidean Network Trajectories: Second-Moment Geometry, Attribution, and Change Points Causal discovery under mean independence and linearity Perturbation is All You Need for Extrapolating Language Models Realizable Bayes-Consistency for General Metric Losses Vanishing L2 regularization for the softmax Multi Armed Bandit Imbalanced Classification under Capacity Constraints Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy On the Optimal Sample Complexity of Offline Multi-Armed Bandits with KL Regularization Extrapolation in Statistical Learning 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probabilistic forecast using MMAF-guided learning The Geometry of Knowing: From Possibilistic Ignorance to Probabilistic Certainty -- A Measure-Theoretic Framework for Epistemic Convergence Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data Conformal Policy Control Continuous-time reinforcement learning: ellipticity enables model-free value function approximation High-accuracy sampling for diffusion models and log-concave distributions Analyzing Shapley Additive Explanations to Understand Anomaly Detection Algorithm Behaviors and Their Complementarity Optimal Lower Bounds for Online Multicalibration Understanding Overparametrization in Survival Models through Interpolation Eventually LIL Regret: Almost Sure $\ln\ln T$ Regret for a sub-Gaussian Mixture on Unbounded Data Limit Theorems for Stochastic Gradient Descent in High-Dimensional Single-Layer Networks Optimal In-context Adaptivity and Distributional Robustness of Transformers Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation The Good, the Bad, and the Sampled: a No-Regret Approach to Safe Online Classification GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms A note on the unique properties of the Kullback--Leibler divergence for sampling via gradient flows Multi-Armed Bandits With Machine Learning-Generated Surrogate Rewards Efficient compression of neural networks and datasets Out-of-Distribution Generalization of In-Context Learning: A Low-Dimensional Subspace Perspective Super-fast Rates of Convergence for Neural Network Classifiers under the Hard Margin Condition Sharp Gaussian approximations for Decentralized Federated Learning Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels Smoothed Analysis of Learning from Positive Samples Statistical Impossibility and Possibility of Aligning LLMs with Human Preferences: From Condorcet Paradox to Nash Equilibrium Sharp Risk Bounds for Early-Stopping in Gaussian Linear Regression Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent Copula-enhanced Vision Transformer for high myopia diagnosis through OU UWF fundus images General Frameworks for Conditional Two-Sample Testing Improved Hardness Results for Learning Intersections of Halfspaces Consistency of Lloyd's Algorithm Under Perturbations Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation Distribution-Free Stochastic Analysis and Robust Multilevel Vector Field Anomaly Detection Efficient Parameter Estimation of Truncated Boolean Product Distributions
Weighted Tail Random Variable: A Novel Framework with Stochastic Properties and Applications
Sarikul Islam, Nitin Gupta · 2025-05-26 · via math.ST updates on arXiv.org

This paper introduces a novel framework to construct the probability density function (PDF) of non-negative continuous random variables. The proposed framework uses two functions: one is the survival function (SF) of a non-negative continuous random variable, and the other is a weight function, which is an increasing and differentiable function satisfying some properties. The resulting random variable is referred to as the weighted tail random variable (WTRV) corresponding to the given random variable and the weight function. We investigate several reliability properties of the WTRV and establish various stochastic orderings between a random variable and its WTRV, as well as between two WTRVs. Using this framework, we construct a WTRV of the Kumaraswamy distribution. We conduct goodness-of-fit tests for two real-world datasets, applied to the Kumaraswamy distribution and its corresponding WTRV. The test results indicate that the WTRV offers a superior fit compared to the Kumaraswamy distribution, which demonstrates the utility of the proposed framework.

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