The Lomax distribution, which is often used to describe severe losses and financial risks because of its heavy tail features, is the basis distribution of the shifted Lomax (SHL-X) family of distributions that we propose in this study. The main objective is to increase the adaptability and accuracy of the traditional Lomax model in the representation of complex data sets. We explore various mathematical properties of the special member called the shifted Lomax Weibull (SHL-W), including its moments, quantile function and entropy measures. We employ the maximum likelihood estimation approach to estimate the parameters of the SHL-W distribution. Simulation studiesare conducted to evaluate the estimators’ accuracy and dependability. The practical applicability of the proposed model is demonstrated by its application to insurance data, highlighting its effectiveness in modeling claims and determining appropriate premium rates.The findings highlight the new model’s potential for broader applications in risk management and financial analysis by showing that it is more data-adapted than competing models.

Here, we present a new bounded distribution known as the power Lambert uniform distribution, and we deduce some of its statistical properties such as quantile function, moments, incomplete moments, mean residual life and mean inactivity time, Lorenz, Bonferroni, and Zenga curves, and order statistics. We presented different shapes of the probability density function and the hazard function of the proposed model. Eleven traditional methods are used to estimate its parameters. The behavior of these estimators is investigated using simulation results. Some actuarial measures are derived mathematically for our proposed model. Some numerical computations for these actuarial measures are given for some choices of parameters and significance levels. A new quantile regression model is constructed based on the new unit distribution. The maximum likelihood estimation method is used to estimate the unknown parameters of the regression model. Furthermore, the usability of the new distribution and regression models is demonstrated with the COVID-19 and educational datasets, respectively.

We introduced a brand-new member of the family that is going to be referred to as the New Power Topp-Leone Generated (NPTL-G). This new member is one of a kind. Given the major functions that created this new member, important mathematical aspects are discussed in as much detail as possible. We derived some functions for the new one, included the Rényi entropy, the qf, series development, and moment weighted probabilities. Moreover, to estimate the values of the parameters of our model that were not known, we employed the maximum likelihood technique. In addition, two actual datasets from the real world were investigated in order to bring attention to the possible applications of this novel distribution. This new model performs better than three key rivals based on the measurements that were collected.

Coronavirus disease (COVID-19) onset in December 2019 is a contagious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since, the spread of the virus and mortality due to COVID-19 have continued to increase daily leading to a pandemic. In absence of approved medicine and vaccines, many countries imposed policies such as social distancing, mask wearing, hand washing, airport screening, quarantine and others. But rapidly, they were confronted with the high economic and social cost resulting from those policies. Many vaccines have been proposed but their efficiency is still controversial. Now, governments and scholars search for how manage with preventives measures policies and vaccination campaigns to stop the COVID-19 spread. This work studied the effects of these different strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contribution in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number was computed with and without respect of preventives measures. The optimal control analysis was carried out using the Pontryagin’s maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings revealed that the optimal implementation of preventive measures reduce highly the number of infected individuals but zero infection was not achieved in the population. That was obtained with the optimal implementation of vaccination campaigns which reduce the number of infected individuals. But the optimal and combined implementation of the two interventions performed better with less costs than the two singular implementations.

Researchers have been working with different models to forecast COVID-19 cases. Many of their estimates are not accurate. This study aims to propose the best model to forecast COVID-19 cumulative cases using a machine learning technic. It is a work that focused on time series univariate models because there are too many debates about the quality of the pandemic data. To increase the likelihood of the findings, we avoided many variables modeling and proposed a robust process to forecast COVID-19 cumulative cases. It will help international institutions to take optimal decisions about the world economy and response to the pandemic. Consequently, we used the data titled “Coronavirus Pandemic (COVID-19)” from “Our World in Data” about cases from 22 January 2020 to 30 November 2020. We computed Error Trend Season (ETS), Exponential smoothing with multiplicative error-trend, and ARIMA on the training data sets. In addition, we calculated the Mean Absolute Percentage Error (MAPE) per model. Among those models, we notice that ETS (with additive error-trend and no season) has the smallest MAPE statistics compared to the others. The findings revealed that with the ETS model we need at least 100 days to have good forecasts with a MAPE threshold of 1%.

In this paper, a new flexible two-parameter family of distributions is introduced. Some mathematical properties, such as asymptotic behavior, moments, stochastic order, entropy, and quantile function, are examined. A special case of this family is introduced called Gemeay–Zeghdoudi distribution. The unknown parameters of the Gemeay–Zeghdoudi distribution are estimated via many estimators. The efficiency of the estimators is compared with a Monte Carlo simulation. The applicability of the new distribution is illustrated by the annual maximum flood and survival times of patients with breast cancer real data analyses.