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洛马克斯切线广义分布族：特性、模拟及在水文强度数据上的应用

Lomax tangent generalized family of distributions: Characteristics, simulations, and applications on hydrological-strength data.

作者信息

Zaidi Sajid Mehboob, Mahmood Zafar, Atchadé Mintodê Nicodème, Tashkandy Yusra A, Bakr M E, Almetwally Ehab M, Hussam Eslam, Gemeay Ahmed M, Kumar Anoop

机构信息

Department of Statistics, Govt. Graduate College B.R., Bahawalpur, Pakistan.

Government SE Graduate college Bahawalpur, Bahawalpur, Pakistan.

出版信息

Heliyon. 2024 May 31;10(12):e32011. doi: 10.1016/j.heliyon.2024.e32011. eCollection 2024 Jun 30.

DOI:10.1016/j.heliyon.2024.e32011
PMID:39183875
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11341239/
Abstract

This article proposes and discusses a novel approach for generating trigonometric G-families using hybrid generalizers of distributions. The proposed generalizer is constructed by utilizing the tangent trigonometric function and distribution function of base model . The newly proposed family of uni-variate continuous distributions is named the "Lomax Tangent Generalized Family of Distributions (LT-G)" and structural-mathematical-statistical properties are derived. Some special and sub-models of the proposed family are also presented. A Weibull-based model, 'The Lomax Tangent Weibull (LT-W) Distribution," is discussed and the plots of density (pdf) and hazard (hrf) functions are also explained. Model parameter estimates are estimated by employing the maximum likelihood estimation (MLE) procedure. The accuracy of the MLEs is evaluated through Monte Carlo simulation. Last but not least, to demonstrate the flexibility and potential of the proposed distribution, two actual hydrological and strength data sets are analyzed. The obtained results are compared with well-known, competitive, and related existing distributions.

摘要

本文提出并讨论了一种使用分布的混合泛化器生成三角G族的新方法。所提出的泛化器是通过利用基础模型的正切三角函数和分布函数构建的。新提出的单变量连续分布族被命名为“洛马克斯正切广义分布族（LT-G）”，并推导了其结构-数学-统计性质。还给出了该族的一些特殊模型和子模型。讨论了一个基于威布尔的模型，即“洛马克斯正切威布尔（LT-W）分布”，并解释了密度（pdf）和风险（hrf）函数的图。通过采用最大似然估计（MLE）程序来估计模型参数。通过蒙特卡罗模拟评估最大似然估计的准确性。最后但同样重要的是，为了证明所提出分布的灵活性和潜力，分析了两个实际的水文和强度数据集。将所得结果与著名的、有竞争力的和相关的现有分布进行了比较。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/a7de56252981/gr010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/ad7e6257f96f/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/8c4915b71922/gr002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/5b7eb1ae106e/gr003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/40ebfdd4d1ef/gr004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/e6a8f0f138d3/gr005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/577fbd436fd6/gr006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/93c5b89a755b/gr007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/3a2f9da24802/gr008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/70a8863b8a4f/gr009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/a7de56252981/gr010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/ad7e6257f96f/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/8c4915b71922/gr002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/5b7eb1ae106e/gr003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/40ebfdd4d1ef/gr004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/e6a8f0f138d3/gr005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/577fbd436fd6/gr006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/93c5b89a755b/gr007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/3a2f9da24802/gr008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/70a8863b8a4f/gr009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9ba3/11341239/a7de56252981/gr010.jpg

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