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In this paper, a five-parameter distribution, Khalil’s new generalized Weibull distribution, is defined and studied in detail. Some mathematical and statistical functions are studied. The effects of shape parameters on skewness and kurtosis are studied. Extensions for density and distribution functions are provided. Estimation of the intended model parameters based on ranked samples is investigated. The behavior of the maximum likelihood estimators is examined using a Monte Carlo simulation. In order to predict unique symmetric and asymmetric patterns and illustrate the applicability and potential of the intended distribution, a COVID-19 dataset is analyzed. The goodness-of-fit results of the new generalized Weibull model of Khalil are compared with some other models. Finally, we make some concluding remarks.

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In this paper, by including a trigonometric function, we propose a family of heavy-tailed distribution called the arcsine Kumaraswamy generalized-X family of distributions. Based on the proposed approach, a four-parameter extension of the Lomax distribution called the arcsine Kumaraswamy generalized Lomax (ASKUG-LOMAX) distribution is discussed in detail. Maximum likelihood, bootstrap, and Bayesian estimation are used to estimate the model parameters. A simulation study is used to evaluate ASKUG-LOMAX performance. The flexibility and usefulness of the proposed ASKUG-LOMAX distribution to predict unique symmetric and asymmetric patterns is demonstrated by analyzing real data. The results show that the ASKUG-LOMAX model is a good candidate for analyzing claims based on heavy-tailed data.