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In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and Lmoment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences. [ABSTRACT FROM AUTHOR]

In this paper, a new flexible generator of distributions is proposed. Some of its fundamental properties including quantile, skewness, kurtosis, hazard rate function, moments, mean deviations, mean time to failure, mean time between failure, availability and reliability function of consecutive linear and circular systems are studied. The hazard rate function can be increasing, decreasing, unimodal-bathtub, unimodal, bathtub, J and inverse J-shaped depending on its parameters values. After introducing the general class, two special models of the new family are discussed in detail. Maximum likelihood and Bayesian methods are used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. We also illustrate the importance of the new family by means of two distinctive real data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive and negative real data in many areas. [ABSTRACT FROM AUTHOR]

The current epidemic outbreak COVID-19 first took place in the Wuhan city of China and then spread worldwide. This deadly disease affected millions of people and compelled the governments and other concerned institutions to take serious actions. Around 0.28 million people have died from the COVID-19 outbreak as of May 11, 2020, 05:41 GMT, and the number is still increasing exponentially. The results of any scientific investigation of this phenomenon are still to come. However, now it is urgently needed to evaluate and compare the disease dynamics to improve the quarantine activities and the level of individual protection, to at least speed up the rate of isolation of infected persons. In the domain of big data science and other related areas, it is always of interest to provide the best description of the data under consideration. Therefore, in this article, we compare the COVID-19 pandemic dynamics between two neighboring Asian countries, Iran and Pakistan, to provide a framework to arrange the appropriate quarantine activities. Simple tools for comparing this deadly pandemic dynamic have been presented that can be adopted to produce the bases for inferences. Most importantly, a new statistical model is developed to provide the best description of COVID-19 daily deaths data in Iran and Pakistan. [ABSTRACT FROM AUTHOR]

This paper introduces a new univariate fl exible generator of distributions called the odd Chen-G family, and some of its statistical properties are derived. Two special models of the proposed generator are provided. The model parameters are estimated using six estimation methods, namely, maximum likelihood estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, Cramér-von Mises estimators and percentile based estimators. Further, simulations are performed to compare their performances for both small and large samples. Finally, two real datasets are used to illustrate the fl exibility of the special models of the proposed family. [ABSTRACT FROM AUTHOR]

This paper introduces a new two-parameter exponentiated discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, stress–strength reliability, mean residual lifetime, mean past lifetime, order statistics and L-moment statistics. The hazard rate function can be increasing, decreasing, decreasing–increasing–decreasing, increasing–decreasing–increasing, unimodal, bathtub, and J-shaped depending on its parameters values. Two methods are used herein to estimate the model parameters, namely, the maximum likelihood, and the proportion. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and proportion estimators. The flexibility of the proposed model is explained by using four distinctive data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive real data in many areas. [ABSTRACT FROM AUTHOR]

In this paper, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation forced by multiplicative noise. To obtain the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation, we apply the G ′ G -expansion method. Furthermore, we generalize some previous results that did not use this equation with multiplicative noise and fractional space. Additionally, we show the influence of the stochastic term on the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation. [ABSTRACT FROM AUTHOR]

The importance of biomedical physical data is underscored by its crucial role in advancing our comprehension of human health, unraveling the mechanisms underlying diseases, and facilitating the development of innovative medical treatments and interventions. This data serves as a fundamental resource, empowering researchers, healthcare professionals, and scientists to make informed decisions, pioneer research, and ultimately enhance global healthcare quality and individual well-being. It forms a cornerstone in the ongoing pursuit of medical progress and improved healthcare outcomes. This article aims to tackle challenges in estimating unknown parameters and reliability measures related to the modified Weibull distribution when applied to censored progressive biomedical data from the initial failure occurrence. In this context, the article proposes both classical and Bayesian techniques to derive estimates for unknown parameters, survival, and failure rate functions. Bayesian estimates are computed considering both asymmetric and symmetric loss functions. The Markov chain Monte Carlo method is employed to obtain these Bayesian estimates and their corresponding highest posterior density credible intervals. Due to the inherent complexity of these estimators, which cannot be theoretically compared, a simulation study is conducted to evaluate the performance of various estimation procedures. Additionally, a range of optimization criteria is utilized to identify the most effective progressive control strategies. Lastly, the article presents a medical application to illustrate the effectiveness of the proposed estimators. Numerical findings indicate that Bayesian estimates outperform other estimation methods by achieving minimal root mean square errors and narrower interval lengths., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

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.

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.

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., Competing Interests: The authors have declared that no competing interests exist.

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., Competing Interests: The authors declare that there are no conflicts of interest regarding the publication of this article., (Copyright © 2022 Javid Gani Dar et al.)

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.

In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information due to its usefulness in estimation methods. The current study presents two new estimators for the distribution function of a finite population based on dual auxiliary variables. The new estimators can be used in situations where the researchers face some sort of complex data set. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator. Besides, an empirical study simulation study has also been conducted to analyse the performance of estimators. It is found that the new suggested estimators of the distribution function of a finite population are more accurate than some of the existing estimators.

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., Competing Interests: The authors declare that they have no conflicts of interest., (Copyright © 2022 Mahmoud El-Morshedy et al.)

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., Competing Interests: The authors declare that they have no conflicts of interest., (Copyright © 2022 Mahmoud El-Morshedy et al.)

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., Competing Interests: The authors declare that they have no conflicts of interest., (Copyright © 2022 Muhammad Ahsan-ul-Haq et al.)

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.

Population development of Tylenchulus semipenetrans in dry soil was investigated in a greenhouse study. Citrus seedlings were grown in sandy soil in vertical tubes with upper and lower sections. Nematode population densities in the upper tubes were measured at 16, 23, and 37 days, post-treatment. Three treatments consisted of i) irrigating both tubes when soil water potential reached -1 5 kPa (non-drought), ii) irrigating only the bottom tube (local drought), and iii) no irrigation (uniform drought). Soil water potential in the upper tubes did not differ under local and uniform drought during the first 16 days post-treatment, when it approached - 125 kPa. Thereafter, the water potential of soil under uniform drought continued to decrease, while that under local drought stabilized at approximately -150 kPa. Treatments had no consistent effects on female T. semipenetrans counts from soil or roots. However, after 37 days, numbers of eggs, juvenile, and male nematodes per gram of root under local drought were more than 2.4-fold greater than those under non-drought or uniform drought. Numbers of juvenile and male nematodes in soil were 6.5 times higher under local drought than under non-drought after 37 days. Nematodes did not survive in soil under uniform drought. Most of the eggs recovered on each date, from roots under local and non-drought, hatched within 35 days. Sixteen days of uniform drought reduced cumulative egg hatch to 51%, and almost no eggs hatched after 23 and 37 days of uniform drought. Thus, the response of T. semipenetrans to dry soil is fundamentally different, depending on whether all or part of the rhizosphere experiences drought. These data and field observations suggest that hydraulic lift via the root xylem may prolong the activity of some nematodes and possibly other rhizosphere-inhabiting organisms in dry soil.