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In this paper, we developed a novel superior distribution, demonstrated and derived its mathematical features, and assessed its fuzzy reliability function. The novel distribution has numerous advantages, including the fact that its CDf and PDf have a closed shape, making it particularly relevant in many domains of data science. We used both conventional and Bayesian approaches to make various sorts of estimations. A simulation research was carried out to investigate the performance of the classical and Bayesian estimators. Finally, we fitted a COVID-19 mortality real data set to the suggested distribution in order to compare its efficiency to that of its rivals.

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In this research, we studied the mixture of normal and half-normal distributions and introduced some properties for this mixture. In particular, we derived the mean, median, and mode of the mixture of normal and half-normal distributions. We also focused on exploring the Bayesian estimation of parameters of the mixture of normal and half-normal distributions by using different methods and then, using type-I censored sample units, presented a simulation study on the mixture of normal and half-normal distributions.