## 7 Real Data Applications  
We used the traditional value of criteria (VC) to compare the fit models, such as the Akaike information criterion (AIVC), consistent AIVC (CAIVC), Bayesian information criterion (BIVC), Hannan-Quinn information criterion (HQIVC), Anderson-Darling value (ADV), Cramer-von Mises value (CMV), Kolmogorov-Smirnov distance (KSD), \(p\)-value of Kolmogorov-Smirnov (PKS), and standard error (SE). Our primary statistical goal was to use a fitting approach model to examine three real datasets that are significant in different fields. In this respect, we compared the fit of the proposed UEHLD with that of the unit Weibull (UW), the Kumaraswamy (K), beta (Beta), Kumaraswamy-Kumaraswamy (KK) ([PERSON] and [PERSON] [33]), Marshall-Olkin-Kumaraswamy (MOK) ([PERSON] and [PERSON] [34]), UBKII, and UGLBXII distributions. The effectiveness of the parameter estimator for the UEHLD for the three datasets under consideration was also assessed using the ML, MPS, and Bayesian techniques via the standard error and confidence interval length criteria measures. We obtained the estimators of the new model for three techniques for the datasets under consideration, with the exception of the first dataset, for which the MPS approach was not employed because it has more equal values. For further clarification, the log-likelihood of the suggested model is supplied, along with examples of the contour plots with various parameter values. We also provide plots of the posterior distributions of the parameters, as well as histograms for the marginal posterior density estimates for three datasets. **Dataset I**: The trade share dataset takes into account the values of the trade share variable used in the renowned \"Determinants of Economic Growth Data\". Along with factors that may be associated with growth, the growth rates of up to 61 different countries were taken into consideration. The information is publicly accessible online as an addition to Stock and Watson [35]. The trade share dataset consists of the following numbers: 0.1405, 0.1566, 0.1577, 0.1604, 0.1608, 0.2215, 0.2994, 0.3131, 0.3246, 0.3247, 0.3295, 0.3300, 0.3379, 0.3397, 0.3523, 0.3589, 0.3933, 0.4176, 0.4258, 0.4356, 0.4421, 0.4444, 0.4505, 0.4558, 0.4683, 0.4733, 0.4846, 0.4889, 0.5096, 0.5177, 0.5278, 0.5347, 0.5433, 0.5442, 0.5508, 0.5527, 0.5606, 0.5607, 0.5671, 0.5753, 0.5828, 0.6030, 0.6050, 0.6136, 0.6261, 0.6395, 0.6469, 0.6512, 0.6816, 0.6994, 0.7048, 0.7292, 0.7430, 0.7455, 0.7798, 0.7984, 0.8147, 0.8230, 0.8302, 0.8342, 0.9794. **Dataset II**: This dataset includes 30 measurements of polyester fibers' tensile strength made by [PERSON] and [PERSON] [36]. The data are 0.023, 0.032, 0.054, 0.069, 0.081, 0.094, 0.105, 0.127, 0.148, 0.169, 0.188, 0.216, 0.255, 0.277, 0.311, 0.361, 0.376, 0.395, 0.432, 0.463, 0.481, 0.519, 0.529, 0.567, 0.642, 0.674, 0.752, 0.823, 0.887, 0.926. **Dataset III**: COVID-19 of Britain: This dataset covered a period of 82 days, from 1 May 2021 to 16 July 2021 (see [PERSON] et al. [37]). The following information is created using daily new deaths (DNDs), daily cumulative cases (DCCs), and daily cumulative deaths (DCDs): 0.0023, 0.0023, 0.0023, 0.0046, 0.0065, 0.0067, 0.0069, 0.0069, 0.0091, 0.0093, 0.0093, 0.0011, 0.0115, 0.0116, 0.0116, 0.0119, 0.0133, 0.0136, 0.0138, 0.0138, 0.0159, 0.0161, 0.0162, 0.0162, 0.0163, 0.0180, 0.0187, 0.0202, 0.0207, 0.0208, 0.0225, 0.0230, 0.0230, 0.0239, 0.0245, 0.0251, 0.0255, 0.0255, 0.0255, 0.0257, 0.0275, 0.0295, 0.0297, 0.0300, 0.0302, 0.0312, 0.0314, 0.0326, 0.0346, 0.0349, 0.0350, 0.0355, 0.0379, 0.0384, 0.0394, 0.0394, 0.0412, 0.0419, 0.0425, 0.0461, 0.0464, 0.0468, 0.0471, 0.0495, 0.0501, 0.0521, 0.0571, 0.0588, 0.0597, 0.0628, 0.0679, 0.0685, 0.0715, 0.0766, 0.0780, 0.0942, 0.0960, 0.0988, 0.1223, 0.1343, and 0.1781.