[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124448-en":3,"doc-seo-124448-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},124448,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","A New Family of Generalized Distributions - with Applications and Benchmarking against Machine Learning Models","This study introduces a new family of generalized distributions built on the Lomax tangent generalized transformation. Closed-form expressions are derived for the cumulative distribution function (CDF) and probability density function (PDF). A sub-model, the generalized Lomax tangent transformed exponential (NGLTGE) distribution, is constructed using the exponential distribution as the baseline. Key mathematical properties are investigated, and Monte Carlo simulation verifies good asymptotic behavior of estimators. A group acceptance sampling plan supports quality-control utility, and real datasets from cryptocurrency, COVID-19, and breast cancer demonstrate consistently superior statistical fit versus related distributions.","A New Family of Generalized Distributions, with Applications and Benchmarking against Machine Learning Models  \nBassant Elkalzah 1,2 , Emmanuel E. Oguadimma3 , Victory C. Obieke3 , Chinonso Michael Eze4,* , Okechukwu J. Obulezi5 and Mohammed Elgarhy6,7,8  \n1Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia  \n2Department of Statistics, Mathematics and Insurance, Faculty of Business, Alexandria University, Alexandria, 21526, Egypt  \n3Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA  \n4Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Nigeria  \n5Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, P. O. Box 5025 Awka, Nigeria  \n6Faculty of Computers and Information Systems, Egyptian Chinese University, Nasr City, Egypt 7Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis, AlSharkia, Egypt 8Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkey  \nAbstract: In this study, we introduce a new family of generalized distributions using the Lomax tangent generalized transformation. We derive the general formulas for its cumulative distribution function (CDF) and probability density function (PDF) . As a specific sub-model, we construct the new generalized Lomax tangent transformed exponential (NGLTGE) distribution by using the exponential distribution as the baseline. We investigate the model’s key mathematical properties and conduct a Monte Carlo simulation, which confirms that the estimators exhibit good asymptotic behavior. A group acceptance sampling plan is also designed to demonstrate its utility in quality control. The NGLTGE model is then applied to real-world datasets from cryptocurrency, COVID-19, and breast cancer, where it consistently provides a superior statistical fit compared to related distributions. Finally, we apply the NGLTGE distribution within a machine learning framework using a PyTorch maximum likelihood estimation. The model’s predictive performance is found to be competitive with, and in some cases superior to, state-of-the-art machine learning density estimators like the Log-Gaussian Mixture Model (Log-GMM) and Masked Autoregressive Flow (MAF), especially for data with heavy tails. This work positions the NGLTGE distribution as a valuable, interpretable, and scalable model for both classic statistical and modern data science applications.  \nKeywords: Generalized distributions, Lomax tangent generalized family, Monte Carlo Simulation, Log-Gaussian Mixture Model, Masked Autoregressive Flow.  \n1. INTRODUCTION  \nChoosing the right statistical distribution for adataset is a critical step, as there is often no single, obvious choice. A common , but not always objective, method involves testing multiple distributions and selecting the one that best fits the data, but a more efficient approach is to use a general family of distributions, such as Pearson’s, that can be adjusted to fit a wide range of data [1] . Generalization is a common and fascinating approach to designing new families of distributions. In the end, the structural cum functional form of the based distribution is altered. This often leads to a more robust model with better goodness-of-fit, parameter estimates with minimum standard errors, and tractable characteristics. The new families fashioned this way are known for being able to capture intricate properties of datasets that the parent  \n*Address correspondence to this author at the Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Nigeria;  \nE-mail: [chinonso.eze@unn.edu.ng](chinonso.eze@unn.edu.ng)  \ndistributions could not capture. Such generalizations include the Kumaraswamy generalized family by [2], the log-logistic tangent generalized family by [3], new sine family of generalized distributions by [4], new twoparameter mi","cbCais0Jke56ryqW","https://ap.wps.com/l/cbCais0Jke56ryqW","pdf",2551320,1,34,"English","en",105,"# Introduction\n# Lomax tangent generalized transformation\n## CDF and PDF derivation\n## Quantile function\n# Model construction: NGLTGE\n# Mathematical properties and estimation\n# Monte Carlo simulation\n# Group acceptance sampling plan\n# Applications to real datasets\n# Benchmarking with machine learning models","[{\"question\":\"What new distribution family is proposed in the study?\",\"answer\":\"The study proposes a new family of generalized distributions based on the Lomax tangent generalized transformation, providing general CDF and PDF formulas.\"},{\"question\":\"How is the specific NGLTGE sub-model constructed?\",\"answer\":\"The NGLTGE distribution is built by using the exponential distribution as the baseline within the generalized Lomax tangent transformation framework.\"},{\"question\":\"How is the model validated and benchmarked against machine learning methods?\",\"answer\":\"Validation includes Monte Carlo simulation for estimator behavior and a group acceptance sampling plan for quality control; benchmarking uses a PyTorch maximum likelihood estimation and compares predictive density performance against Log-GMM and MAF, especially for heavy-tailed data.\"}]","A New Family of Generalized Distributions - with Applications and Benchmarking against Machine Learning Models | PDF",1785822342,86,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"a-new-family-of-generalized-distributions-with-applications-and-benchmarking-against-machine-learning-models","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/a-new-family-of-generalized-distributions-with-applications-and-benchmarking-against-machine-learning-models/124448/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What new distribution family is proposed in the study?","Question",{"text":75,"@type":76},"The study proposes a new family of generalized distributions based on the Lomax tangent generalized transformation, providing general CDF and PDF formulas.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the specific NGLTGE sub-model constructed?",{"text":80,"@type":76},"The NGLTGE distribution is built by using the exponential distribution as the baseline within the generalized Lomax tangent transformation framework.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the model validated and benchmarked against machine learning methods?",{"text":84,"@type":76},"Validation includes Monte Carlo simulation for estimator behavior and a group acceptance sampling plan for quality control; benchmarking uses a PyTorch maximum likelihood estimation and compares predictive density performance against Log-GMM and MAF, especially for heavy-tailed data.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]