Squared normal model and its generalization for the analysis of skewed positive data

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Xuanyu Liu, Chi Zhang, Kam Chuen Yuen, Guo-Liang Tian

Published: 2025, Last Modified: 12 Nov 2025Commun. Stat. Simul. Comput. 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: To model skewed positive data with high kurtosis, this paper proposes, a new squared normal (SQN) distribution, which is constructed by squaring the normal random variable with non-zero mean and non-unit variance. The SQN distribution can be regarded as an extension of the chi-squared distribution, which cannot be applied to directly modeling real-life data. Some distributional properties, parameter estimation methods and hypothesis testings are investigated for the SQN distribution itself and the corresponding regression model. Furthermore, a generalization to a squared skew-normal (SSN) distribution is proposed by incorporating an additional skew parameter, improving the flexibility of the model. Finally, simulation experiments are conducted and a real data set is analyzed to demonstrate the proposed methodologies.