Abstract
This research paper introduces a novel two-parameter quadratic exponential distribution, thoroughly examining its statistical properties and practical applications. The study delves into essential characteristics of the distribution, including its asymptotic behavior, moments, order statistics, and entropies. Additionally, we present fuzzy reliability, value at risk, mean excess function, limited expected value function, tail value at risk, and tail variance. A comprehensive simulation study evaluates fifteen parameter estimation methods. To illustrate the practical relevance of the proposed distribution, three sets of real-world data are analyzed. The performance of the proposed distribution model is rigorously assessed using various model selection criteria and goodness-of-fit test statistics. Empirical findings consistently demonstrate the proposed distribution's superiority over existing models, highlighting its potential for multiple applications.
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