The procedures to discover proper new models in probability theory for different data collections are highly prevalent these days among the researchers of this area whenever existing literature models are not appropriate. Before delivering a product, manufacturers of raw materials or finished materials must follow some compliance standards in various engineering disciplines to avoid severe losses. Materials of high strength are necessary to ensure the safety of human lives along with infrastructures to elude the significant obligations linked with the provisions of non-compliant products. Using probability theory, we introduce the weighted version of inverted Kumaraswamy Distribution, which could be considered a better model than some other sub-models used to model Carbon fiber’s strength data. We derive various statistical properties of this distribution such as cumulative distribution, moments, mean residual life, reversed residual life functions, moment generating function, characteristic function, harmonic mean, and geometric mean. Parameters are estimated through the maximum likelihood method and ordinary moments. Simulation studies are carried out to illustrate the theoretical results of these two approaches. Furthermore, two real data sets of Carbon fibers strength are utilized to contrast the proposed model and its sub-models like inverted Kumaraswamy distribution and Kumaraswamy Sushila distribution through different goodness of fit criteria such as Akaike Information Criterion (AIC), corrected Akaike information criterion, and the Bayesian Information Criterion (BIC). Results reveal the outperformance of the proposed model compared to other models, which render it a proper interchange of the current sub-models.

如今，只要不适合现有的文献模型，在该领域的研究人员中就很可能在不同的数据收集概率论中发现合适的新模型。在交付产品之前，原材料或制成品的制造商必须遵守各个工程学科的某些合规性标准，以避免严重损失。为了确保人命安全以及基础设施，必须使用高强度的材料来避免与不合格产品规定相关的重大义务。使用概率论，我们介绍了反向Kumaraswamy分布的加权形式，该模型可以比比其他用于建模碳纤维强度数据的子模型更好。我们推导出该分布的各种统计属性，例如累积分布，矩，平均剩余寿命，反向剩余寿命函数，矩生成函数，特征函数，谐波均值和几何均值。通过最大似然法和普通矩来估计参数。通过仿真研究来说明这两种方法的理论结果。此外，利用两个真实的碳纤维强度数据集，通过不同的拟合标准（例如Akaike信息准则（AIC），修正的Akaike信息准则），对比了所提出的模型及其子模型（如反向Kumaraswamy分布和Kumaraswamy Sushila分布）。和贝叶斯信息准则（BIC）。