In this study, we have focused to propose a flexible model that demonstrates increasing, decreasing and upside-down bathtub-shaped density and failure rate functions. The proposed model refers to as the exponentiated power function (EPF) distribution. Some mathematical and reliability measures are developed and derived. We develop explicit expressions for the moments, quantile function and order statistics. Some shapes of the density and the reliability functions are sketched out and discussed. We suggest the method to estimate the unknown parameters of EPF by the maximum likelihood estimation. Two suitable lifetime datasets from engineering sector are used to explore the dominance of the EPF distribution.

Theoretical and applied researchers have been frequently interested in proposing alternative skewed and symmetric lifetime parametric models that provide greater flexibility in modeling real-life data in several applied sciences. To fill this gap, we introduce a three-parameter bounded lifetime model called the exponentiated new power function (E-NPF) distribution. Some of its mathematical and reliability features are discussed. Furthermore, many possible shapes over certain choices of the model parameters are presented to understand the behavior of the density and hazard rate functions. For the estimation of the model parameters, we utilize eight classical approaches of estimation and provide a simulation study to assess and explore the asymptotic behaviors of these estimators. The maximum likelihood approach is used to estimate the E-NPF parameters under the type II censored samples. The efficiency of the E-NPF distribution is evaluated by modeling three lifetime datasets, showing that the E-NPF distribution gives a better fit over its competing models such as the Kumaraswamy-PF, Weibull-PF, generalized-PF, Kumaraswamy, and beta distributions.

Background: The burden of the spread of the COVID-19 pandemic has impacted widely on the healthcare providers physically and mentally. Many healthcare providers are exposed to psychological stressors due to their high risk of contracting the virus. Aims: This study aimed to measure the level of anxiety among healthcare providers during the COVID-19 pandemic in Saudi Arabia. In addition, this study aimed to measure the level of anxiety based on demographic characteristics. Method: A cross-sectional survey was employed to recruit a convenience sample of healthcare providers. A pencil and paper self-administered questionnaires were used to collect data from demographic and generalized anxiety disorder GAD-7 data. However, this study received written informed consent from participants of the study. In addition, the study was approved by the Institutional Review Board at Dr. Sulaiman Al Habib Medical Group (IRB Log No. RC20.06.88-03). Results: A total of 650 participants were recruited, results of GAD-7 showed that 43.5%, 28.9% and 27.5% of healthcare providers in Saudi Arabia experienced mild, moderate and severe anxiety, respectively, during the COVID-19 pandemic. Results indicated that age, health specialty, nationality, and sleeping disorders before COVID-19 were associated with anxiety levels. Conclusion: The generalized anxiety among healthcare providers in Saudi Arabia was mild. Older healthcare providers were found to have a higher level of anxiety compared to other participating healthcare providers. Several factors may contribute to a higher level of anxiety including age, socioeconomic status, marital status, having chronic conditions, and sleeping disorder before the COVID-19 pandemic. To further understand the level of anxiety among healthcare providers during the COVID-19 pandemic in Saudi Arabia, longitudinal and mixed-method research is needed.

Background: Modeling against non-normal data a challenge for theoretical and applied scientists to choose a lifetime model and expect to perform optimally against experimental, reliability engineering, hydrology, ecology, and agriculture sciences, phenomena. Method: We have introduced a new G class that generates relatively more flexible models to its baseline and we refer to it as the new modified Lehmann Type – II (ML–II) G class of distributions. A list of new members of ML–II-G class is developed and as a sub-model the exponential distribution, known as the ML-II-Exp distribution is considered for further discussion. Several mathematical and reliability characters along with explicit expressions for moments, quantile function, and order statistics are derived and discussed in detail. Furthermore, plots of density and hazard rate functions are sketched out over the certain choices of the parametric values. For the estimation of the model parameters, we utilized the method of maximum likelihood estimation. Results: The applicability of the ML–II–G class is evaluated via ML–II–Exp distribution. ML–II–Exp distribution is modeled to four suitable lifetime datasets and the results are compared with the well-known competing models. Some well recognized goodness–of–fit including -Log-likelihood (-LL), Anderson-Darling (A*), Cramer-Von Mises (W*), and Kolmogorov-Smirnov (K-S) test statistics are considered for the selection of a better fit model. Conclusion: The minimum value of the goodness–of–fit is the criteria of a better fit model that the ML–II–Exp distribution perfectly satisfies. Hence, we affirm that the ML–II–Exp distribution is a better fit model than its competitors.

Background: Modeling with the complex random phenomena that are frequently observed in reliability engineering, hydrology, ecology, medical science, and agricultural sciences was once thought to be an enigma. Scientists and practitioners agree that an appropriate but simple model is the best choice for this investigation. To address these issues, scientists have previously discussed a variety of bounded and unbounded, simple to complex lifetime models. Methods: We discussed a modified Lehmann type II (ML-II) model as a better approach to modeling bathtub-shaped and asymmetric random phenomena. A number of complementary mathematical and reliability measures were developed and discussed. Furthermore, explicit expressions for the moments, quantile function, and order statistics were developed. Then, we discussed the various shapes of the density and reliability functions over various model parameter choices. The maximum likelihood estimation (MLE) method was used to estimate the unknown model parameters, and a simulation study was carried out to evaluate the MLEs' asymptotic behavior. Results: We demonstrated ML- II's dominance over well-known competitors by modeling anxiety in women and electronic data.

Background. A countrys agriculture reflects a backbone and performs a vital part in the betterment of the economy and individuals. Facts and figures of the agriculture sector offer a solid foundation and factual pathway intended for upcoming decisions in favor of a country. Accordingly, the probability models have a more significant influence not only in reliability engineering, hydrology, ecology, and medicine but also in agriculture sciences. Objective. The primary objective of this study is to propose a reliable and efficient model for pearl millet yield analysis, thereby empowering decision-makers to make informed decisions about their farming practices. With the successful implementation of this model, farmers can potentially increase their pearl millet yield, leading to higher incomes and improved livelihoods for the rural population of Pakistan. Model. This study proposes a novel probability model, namely, the alpha transformed odd exponential power function (ATOE-PF) distribution, for analyzing pearl millet yield in Punjab, Pakistan. Data. For data collection, two secondary data sets are explored that are electronically available on the site of the Directorate of Agriculture (Economics and Marketing) Punjab, Lahore, Pakistan. Results. The maximum likelihood estimation technique is used for estimating the model parameters. For the selection of a better fit model, we follow some accredited goodness of fit tests. The efficiency and applicability of the ATOE-PF distribution are discussed over the province of Punjab (with RMSE=4.9176) and Pakistan (with RMSE=4.5849). Better estimates and closest fit to data among the well-established neighboring models offer robust evidence in support of ATOE-PF distribution as well.