Predictive modeling of the COVID-19 data using a new version of the flexible Weibull model and machine learning techniques

Statistical modeling and forecasting of time-to-events data are crucial in every applied sector. For the modeling and forecasting of such data sets, several statistical methods have been introduced and implemented. This paper has two aims, i.e., (i) statistical modeling and (ii) forecasting. For modeling time-to-events data, we introduce a new statistical model by combining the flexible Weibull model with the Z-family approach. The new model is called the Z flexible Weibull extension (Z-FWE) model, where the characterizations of the Z-FWE model are obtained. The maximum likelihood estimators of the Z-FWE distribution are obtained. The evaluation of the estimators of the Z-FWE model is assessed in a simulation study. The Z-FWE distribution is applied to analyze the mortality rate of COVID-19 patients. Finally, for forecasting the COVID-19 data set, we use machine learning (ML) techniques i.e., artificial neural network (ANN) and group method of data handling (GMDH) with the autoregressive integrated moving average model (ARIMA). Based on our findings, it is observed that ML techniques are more robust in terms of forecasting than the ARIMA model.

On the implementation of a new version of the Weibull distribution and machine learning approach to model the COVID-19 data.

Statistical methodologies have broader applications in almost every sector of life including education, hydrology, reliability, management, and healthcare sciences. Among these sectors, statistical modeling and predicting data in the healthcare sector is very crucial. In this paper, we introduce a new method, namely, a new extended exponential family to update the distributional flexibility of the existing models. Based on this approach, a new version of the Weibull model, namely, a new extended exponential Weibull model is introduced. The applicability of the new extended exponential Weibull model is shown by considering two data sets taken from the health sciences. The first data set represents the mortality rate of the patients infected by the coronavirus disease 2019 (COVID-19) in Mexico. Whereas, the second set represents the mortality rate of COVID-19 patients in Holland. Utilizing the same data sets, we carry out forecasting using three machine learning (ML) methods including support vector regression (SVR), random forest (RF), and neural network autoregression (NNAR). To assess their forecasting performances, two statistical accuracy measures, namely, root mean square error (RMSE) and mean absolute error (MAE) are considered. Based on our findings, it is observed that the RF algorithm is very effective in predicting the death rate of the COVID-19 data in Mexico. Whereas, for the second data, the SVR performs better as compared to the other methods.

Statistical analysis of Covid-19 mortality rate via probability distributions.

Among other diseases, Covid 19 creates a critical situation around the world. Five layers have been recorded so far, resulting in the loss of millions of lives in different countries. The virus was thought to be contagious, so the government initially severely forced citizens to keep a distance from each other. Since then, several vaccines have been developed that play an important role in controlling mortality. In the case of Covid-19 mortality, the government should be forced to take significant steps in the form of lockdown, keeping you away or forcing citizens to vaccinate. In this paper, modeling of Covid-19 death rates is discussed via probability distributions. To delineate the performance of the best fitted model, the mortality rate of Pakistan and Afghanistan is considered. Numerical results conclude that the NFW model can be used to predict the mortality rate for Covid-19 patients more accurately than other probability models.

A new statistical approach for modeling the bladder cancer and leukemia patients data sets: Case studies in the medical sector.

Statistical methods are frequently used in numerous healthcare and other related sectors. One of the possible applications of the statistical methods is to provide the best description of the data sets in the healthcare sector. Keeping in view the applicability of statistical methods in the medical sector, numerous models have been introduced. In this paper, we also introduce a novel statistical method called, a new modified-G family of distributions. Several mathematical properties of the new modified-G family are derived. Based on the new modified-G method, a new updated version of the Weibull model called, a new modified-Weibull distribution is introduced. Furthermore, the estimators of the parameters of the new modified-G distributions are also obtained. Finally, the applicability of the new modified-Weibull distribution is illustrated by analyzing two medical sets. Using certain analytical tools, it is observed that the new modified-Weibull distribution is the best choice to deal with the medical data sets.

Statistical Analysis of the COVID-19 Mortality Rates with Probability Distributions: The Case of Pakistan and Afghanistan.

The COVID-19 pandemic has shocked nations due to its exponential death rates in various countries. According to the United Nations (UN), in Russia, there were 895, in Mexico 303, in Indonesia 77, in Ukraine 317, and in Romania 252, and in Pakistan, 54 new deaths were recorded on the 5th of October 2021 in the period of months. Hence, it is essential to study the future waves of this virus so that some preventive measures can be adopted. In statistics, under uncertainty, there is a possibility to use probability models that leads to defining future pattern of deaths caused by COVID-19. Based on probability models, many research studies have been conducted to model the future trend of a particular disease and explore the effect of possible treatments (as in the case of coronavirus, the effect of Pfizer, Sinopharm, CanSino, Sinovac, and Sputnik) towards a specific disease. In this paper, varieties of probability models have been applied to model the COVID-19 death rate more effectively than the other models. Among others, exponentiated flexible exponential Weibull (EFEW) distribution is pointed out as the best fitted model. Various statistical properties have been presented in addition to real-life applications by using the total deaths of the COVID-19 outbreak (in millions) in Pakistan and Afghanistan. It has been verified that EFEW leads to a better decision rather than other existing lifetime models, including FEW, W, EW, E, AIFW, and GAPW distributions.

One- and Two-Sample Predictions Based on Progressively Type-II Censored Carbon Fibres Data Utilizing a Probability Model.

New Weibull-Pareto distribution is a significant and practical continuous lifetime distribution, which plays an important role in reliability engineering and analysis of some physical properties of chemical compounds such as polymers and carbon fibres. In this paper, we construct the predictive interval of unobserved units in the same sample (one sample prediction) and the future sample based on the current sample (two-sample prediction). The used samples are generated from new Weibull-Pareto distribution due to a progressive type-II censoring scheme. Bayesian and maximum likelihood approaches are implemented to the prediction problems. In the Bayesian approach, it is not easy to simplify the predictive posterior density function in a closed form, so we use the generated Markov chain Monte Carlo samples from the Metropolis-Hastings technique with Gibbs sampling. Moreover, the predictive interval of future upper-order statistics is reported. Finally, to demonstrate the proposed methodology, both simulated data and real-life data of carbon fibres examples are considered to show the applicabilities of the proposed methods.

Asymmetric Power Hazard Distribution for COVID-19 Mortality Rate under Adaptive Type-II Progressive Censoring: Theory and Inferences.

This article investigates the estimation of the parameters for power hazard function distribution and some lifetime indices such as reliability function, hazard rate function, and coefficient of variation based on adaptive Type-II progressive censoring. From the perspective of frequentism, we derive the point estimations through the method of maximum likelihood estimation. Besides, delta method is implemented to construct the variances of the reliability characteristics. Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under squared error and linear exponential loss functions. Also, the corresponding credible intervals are constructed. A simulation study is utilized to assay the performance of the proposed methods. Finally, a real data set of COVID-19 mortality rate is analyzed to validate the introduced inference methods.

Poisson XLindley Distribution for Count Data: Statistical and Reliability Properties with Estimation Techniques and Inference.

In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties including order statistics, hazard rate function, reversed hazard rate function, mode, factorial moments, probability generating function, moment generating function, index of dispersion, Shannon entropy, Mills ratio, mean residual life function, and associated measures are investigated. All these properties can be expressed in explicit forms. It is found that the new probability mass function can be utilized to model positively skewed data with leptokurtic shape. Moreover, the new discrete distribution is considered a proper tool to model equi- and over-dispersed phenomena with increasing hazard rate function. The distribution parameter is estimated by different six estimation approaches, and the behavior of these methods is explored using the Monte Carlo simulation. Finally, two applications to real life are presented herein to illustrate the flexibility of the new model.

Bayesian and Frequentist Inferences on a Type I Half-Logistic Odd Weibull Generator with Applications in Engineering.

In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.