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<p>Created page with &quot; == Abstract == &lt;p&gt;This paper introduces the New Extended Topp–Leone (NExTL) distribution, a flexible three-parameter probability model for data on the unit interval (0...&quot;</p> <p><b>New page</b></p><div><br /> == Abstract ==<br /> <br /> &lt;p&gt;This paper introduces the New Extended Topp&amp;ndash;Leone (NExTL) distribution, a flexible three-parameter probability model for data on the unit interval (0, 1). Developed using a type 2 exponentiation framework, it generalizes the classical Topp&amp;ndash;Leone family, offering enhanced versatility in capturing various density shapes and hazard rate behaviors. We derive its core statistical properties, including moments, quantile and hazard functions, entropy measures, and order statistics. Parameter estimation via maximum likelihood is confirmed as consistent and reliable through simulation studies. For practical application, the NExTL distribution is integrated within the generalized additive models for location, scale, and shape (GAMLSS) framework, enabling comprehensive regression modeling of bounded responses. The model&amp;rsquo;s superior performance is empirically validated in two applications: a risk analysis of petroleum rock permeability data, where it provides the best fit and robust tailrisk quantification (Value at Risk and Tail Value at Risk), and a quantile regression analysis of behavioral ecology data, successfully identifying significant treatment effects on insect attraction. In both cases, the NExTL distribution outperforms standard competitors such as the beta and Kumaraswamy distributions, as measured by information criteria and goodness-of-fit statistics, representing a significant advancement for modeling proportional data in fields like engineering, finance, and biology.OPEN ACCESS Received: 13/02/2026 Accepted: 23/06/2026 Published: 07/08/2026&lt;/p&gt;<br /> <br /> <br /> <br /> == Document ==<br /> &lt;pdf&gt;Media:Draft_content_238379350-1046-document.pdf&lt;/pdf&gt;</div>

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