A bivariate distribution based on squared normal transformation

Autor/innen

Lan-Xin Li
National Key Laboratory of Bridge Safety and Resilience, Beijing University of Technology, Beijing 100124, China
Xuan-Yi Zhang
National Key Laboratory of Bridge Safety and Resilience, Beijing University of Technology, Beijing 100124, China
https://orcid.org/0000-0002-2049-236X
Yan-Gang Zhao
National Key Laboratory of Bridge Safety and Resilience, Beijing University of Technology, Beijing 100124, China
https://orcid.org/0000-0002-7975-4918
DOI: https://doi.org/10.17877/tudobooks-11.177

Über dieses Buch

Modeling non-Gaussian dependent random variables remains challenging in structural reliability analysis. This study proposes a bivariate squared normal (BSN) distribution based on the squared normal transformation (SNT). The joint cumulative distribution function (JCDF) is constructed by decomposing the probability into marginal distributions and a dependence function, both modeled using SNT. A power transformation with an optimized parameter is introduced to align the kurtosis of the transformed variable with that of a squared normal reference distribution, improving accuracy for strongly non-Gaussian cases. The joint probability density function (JPDF) is obtained by applying a central difference scheme to the JCDF. Validation against typical bivariate distributions, including classical and copula-based models, shows that the BSN distribution achieves high JCDF accuracy and acceptable JPDF accuracy, demonstrating strong flexibility and robustness across diverse dependence structures.

REC 2026 Reliability Computations in a Data and Model-Driven World

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REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World

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153-162

Veröffentlicht

21.08.2026
Copyright (c) 2026 Matthias Faes, Michael Beer, Julian Behrend, Marco Broccardo, Guohai Chen, Hanshu Chen, Jieyu Chen, Fang Cong, Henrik Ebel, Peter Eberhard, Andrea Franchini, Zhuojia Fu, Yanzhao Gu, Michael Hanss, Hui Huang, Md Maidul Islam, Jafar Jafari-Asl, Balsa Jovanovic, Tom Könecke, Olga Kosheleva, Vladik Kreinovich, Hao-Ming Li, Pei-Pei Li, Qinghe Li, Ruikun Li, Stefano Marelli, Rafi L. Muhanna, Robert L. Mullen, Chiara Nardin, Lukáš Novák, Shenghao Piao, Mario Rosenfelder, Styfen Schär, Jan Schneider, Wei Shi, Panagiotis Spyridis, Bruno Sudret, Ruben Van Coile, Bo-Yu Wang, Dixiong Yang, Xuan-Yi Zhang, Zi-Xin Zhang, Bo-Qi Zhao, Yan-Gang Zhao, Zhibao Zheng, Baihong Zhong, Zhaowei Zhou, Marcos A. Valdebenito, Chao Dang, Lan-Xin Li, Marius Bittner, Parth Tambat, Marco Behrendt, Zhao Liu, Ping Zhu, Zlatan Dimitrov, Petar O. Hristov, Meng-Ze Lyu, Yang-Yi Liu, Jian-Bing Chen, Qitian Lu, Miroslav Vořechovský, Ekaterina Auer, Lorenz Gillner, Julien Alexandre dit Sandretto, Binod K. Yadav, Ghifari Adam Faza, Hans Hallez, David Moens, Reza Naeimaei, Steffen Schön, Elisabeth Ötsch, Hans Neuner, Zhanhua Liang, Jingwen Song, Michael Desch, Mehdi Modares, Valentin Nikolov, Paulo Lucas Figueiredo, José Torres Farinha, Hugo Raposo, António J. Marques Cardoso, Alice do Carmo Duarte Rodrigues, Paula Gonçalves, Peihan Chen, Xinyu Zhu, Pengfei Wei, Kaiwen Li, Mansoureh Shahabi, Y. F. Cui, Johannes O. Royset, Salvatore Russotto, Mario Di Paola, Antonina Pirrotta, Til Lux, Johannes Sundheim, Tania Feiri, Udo Wiens, Marcus Ricker, F. Niklas Schietzold, Felix Harazin, Yoshi Diepelt, Wolfgang Graf, Michael Kaliske, Rongyao Song, Changcong Zhou, Xuanyi Zhao, Weiping Zhang, Juntao Hu, Yu Chen, Edoardo Patelli, Tingting Sun, Jianbing Chen, Bouwe Verkens, L. Bogaerts, Patrick Van Rymenant, Maximilian Schweizer, Marc Fina, Werner Wagner, Steffen Freitag, George Stefanou, Dimitros Savvas, Panagiotis Gavalas, Luigi Schiano, Razhan S. Ahmed, Oleksandr Al-Shboul, David Ringeloth, Vladislav Gudžulić, Stefanie Schoen, Jelena Bijeljić, Ernst Niederleithinger, Iurie Curoşu, Gerrit E. Neu, Jia-Hui Fu, Yi Luo, De-Cheng Feng, Xiao-Qiu Ai, Luyi Li, Hao Wang, Tairan Wang, Sifeng Bi, Emily Zeller (Kapitelautor/in)

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Creative Commons License

Dieses Werk steht unter der Lizenz Creative Commons Namensnennung 4.0 International.

Zitationsvorschlag

A bivariate distribution based on squared normal transformation. (2026). In REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World (pp. 153-162). TUDObooks. https://doi.org/10.17877/tudobooks-11.177