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The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences: notably, lifetime, medical, and financial sciences. This paper introduces a heavy-tailed Nadarajah Haghighi model by compounding the heavy-tailed family and Nadarajah Haghighi distribution. The model obtained has three parameters that account for the scale and shape of the distribution. The proposed distribution's fundamental characteristics, such as the probability density, cumulative distribution, hazard rate, and survival functions, are provided, several key statistical properties are established, and several entropy information measures are proposed. Estimation of model parameters is performed via a maximum likelihood estimator procedure. Further, different simulation experiments are conducted to demonstrate the proposed estimator's performance using measures like the average estimate, the average bias, and the associated mean square error. Finally, we apply our proposed model to analyze three different real datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing models. [ABSTRACT FROM AUTHOR]

The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric, skewed, and complex datasets. The proposed model is obtained by compounding the exponential and XLindley distributions, and it is regarded as a strong competitor for the widely applied symmetrical and non-symmetrical models. Several characteristics and statistical properties are investigated. The unknown parameters of the recommended model for the complete sample are estimated using two estimation methods; notably, maximum likelihood estimation and Bayes techniques based on several loss functions as well as an approximate tool are used to construct the confidence intervals for the unknown parameters of the suggested model. The estimation procedures are compared using a Monte Carlo simulation experiment to demonstrate their effectiveness. In the end, the applicability and flexibility of the recommended model are conducted using two real lifetime datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing distributions. [ABSTRACT FROM AUTHOR]