An enhanced estimator of finite population variance using two auxiliary variables under simple random sampling

In this article, we have suggested a new improved estimator for estimation of finite population variance under simple random sampling. We use two auxiliary variables to improve the efficiency of estimator. The numerical expressions for the bias and mean square error are derived up to the first order approximation. To evaluate the efficiency of the new estimator, we conduct a numerical study using four real data sets and a simulation study. The result shows that the suggested estimator has a minimum mean square error and higher percentage relative efficiency as compared to all the existing estimators. These findings demonstrate the significance of our suggested estimator and highlight its potential applications in various fields. Theoretical and numerical analyses show that our suggested estimator outperforms all existing estimators in terms of efficiency. This demonstrates the practical value of incorporating auxiliary variables into the estimation process and the potential for future research in this area.

Estimation of finite population mean using double sampling under probability proportional to size sampling in the presence of extreme values

Values that are too large or small enough can be found in many data sets. Therefore, the estimator can yield ambiguous findings if several of the incredible deals are picked for the sample. When such extreme values occur, we propose improved estimators to determine the finite population means using double sampling based on probability proportional to size sampling (PPS). The properties of estimators are obtained up to the first order of approximations. When the size of the units varies widely, the PPS sampling technique may be employed. To determine the values of Pi when using PPS, we must be acquainted with the aggregate of the auxiliary variable X i . However the designs and estimation techniques we have looked at so far are unsuccessful and are less effective when this information is difficult to locate or when other information is missing. The two-phase approach is preferable and more feasible in these kinds of circumstances. To demonstrate how effectively the recommended estimators performed, we used three actual data sets. We show mathematically and theoretically that the suggested estimators outperform alternative estimators.

Inverse Unit Teissier Distribution: Theory and Practical Examples

In this paper, we emphasize a new one-parameter distribution with support as [1,+∞). It is constructed from the inverse method applied to an understudied one-parameter unit distribution, the unit Teissier distribution. Some properties are investigated, such as the mode, quantiles, stochastic dominance, heavy-tailed nature, moments, etc. Among the strengths of the distribution are the following: (i) the closed-form expressions and flexibility of the main functions, and in particular, the probability density function is unimodal and the hazard rate function is increasing or unimodal; (ii) the manageability of the moments; and, more importantly, (iii) it provides a real alternative to the famous Pareto distribution, also with support as [1,+∞). Indeed, the proposed distribution has different functionalities but also benefits from the heavy-right-tailed nature, which is demanded in many applied fields (finance, the actuarial field, quality control, medicine, etc.). Furthermore, it can be used quite efficiently in a statistical setting. To support this claim, the maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, Cramér–Von Mises, least squares, weighted least-squares, maximum product of spacing, minimum spacing absolute distance, and minimum spacing absolute-log distance estimation methods are examined to estimate the unknown unique parameter. A Monte Carlo simulation is used to compare the performance of the obtained estimates. Additionally, the Bayesian estimation method using an informative gamma prior distribution under the squared error loss function is discussed. Data on the COVID mortality rate and the timing of pain relief after receiving an analgesic are considered to illustrate the applicability of the proposed distribution. Favorable results are highlighted, supporting the importance of the findings.

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.

Modeling and Forecasting Monkeypox Cases Using Stochastic Models

BACKGROUND

Monkeypox virus is gaining attention due to its severity and spread among people. This study sheds light on the modeling and forecasting of new monkeypox cases. Knowledge about the future situation of the virus using a more accurate time series and stochastic models is required for future actions and plans to cope with the challenge.

METHODS

We conduct a side-by-side comparison of the machine learning approach with the traditional time series model. The multilayer perceptron model (MLP), a machine learning technique, and the Box-Jenkins methodology, also known as the ARIMA model, are used for classical modeling. Both methods are applied to the Monkeypox cumulative data set and compared using different model selection criteria such as root mean square error, mean square error, mean absolute error, and mean absolute percentage error.

RESULTS

With a root mean square error of 150.78, the monkeypox series follows the ARIMA (7,1,7) model among the other potential models. Comparatively, we use the multilayer perceptron (MLP) model, which employs the sigmoid activation function and has a different number of hidden neurons in a single hidden layer. The root mean square error of the MLP model, which uses a single input and ten hidden neurons, is 54.40, significantly lower than that of the ARIMA model. The actual confirmed cases versus estimated or fitted plots also demonstrate that the multilayer perceptron model has a better fit for the monkeypox data than the ARIMA model.

CONCLUSIONS AND RECOMMENDATION

When it comes to predicting monkeypox, the machine learning method outperforms the traditional time series. A better match can be achieved in future studies by applying the extreme learning machine model (ELM), support vector machine (SVM), and some other methods with various activation functions. It is thus concluded that the selected data provide a real picture of the virus. If the situations remain the same, governments and other stockholders should ensure the follow-up of Standard Operating Procedures (SOPs) among the masses, as the trends will continue rising in the upcoming 10 days. However, governments should take some serious interventions to cope with the virus.

LIMITATION

In the ARIMA models selected for forecasting, we did not incorporate the effect of covariates such as the effect of net migration of monkeypox virus patients, government interventions, etc.

Inference for a Kavya–Manoharan Inverse Length Biased Exponential Distribution under Progressive-Stress Model Based on Progressive Type-II Censoring

In this article, a new one parameter survival model is proposed using the Kavya–Manoharan (KM) transformation family and the inverse length biased exponential (ILBE) distribution. Statistical properties are obtained: quantiles, moments, incomplete moments and moment generating function. Different types of entropies such as Rényi entropy, Tsallis entropy, Havrda and Charvat entropy and Arimoto entropy are computed. Different measures of extropy such as extropy, cumulative residual extropy and the negative cumulative residual extropy are computed. When the lifetime of the item under use is assumed to follow the Kavya–Manoharan inverse length biased exponential (KMILBE) distribution, the progressive-stress accelerated life tests are considered. Some estimating approaches, such as the maximum likelihood, maximum product of spacing, least squares, and weighted least square estimations, are taken into account while using progressive type-II censoring. Furthermore, interval estimation is accomplished by determining the parameters’ approximate confidence intervals. The performance of the estimation approaches is investigated using Monte Carlo simulation. The relevance and flexibility of the model are demonstrated using two real datasets. The distribution is very flexible, and it outperforms many known distributions such as the inverse length biased, the inverse Lindley model, the Lindley, the inverse exponential, the sine inverse exponential and the sine inverse Rayleigh model.

Statistical Analysis of the People Fully Vaccinated against COVID-19 in Two Different Regions

Motivation. Currently, the COVID-19 pandemic represents a critical issue all over the world. On May 11, 2020, at 05 : 41 GMT, approximately 0.28 million individuals had perished because of the COVID-19 pandemic, and the figure is continuously growing rapidly. Unfortunately, millions of people have died due to this pandemic. As a result, this issue forced governments and other corresponding organizations to take significant action, such as the lockdown and vaccinations. Furthermore, scientists have developed several vaccinations, and the World Health Organization (WHO) has urged governments and people to get vaccinated to eradicate this pandemic. Consequently, the findings of any scientific research into this phenomenon are highly interesting. Problem Statement. To enhance individual protection, it is now critical to analyze and compare the percentage of people fully vaccinated against COVID-19. It is constantly of interest in the field of big data science and other related disciplines to provide the best analysis and modeling of COVID-19 data. Methodology. Through this paper, we aimed to compare individuals who have been completely vaccinated against COVID-19 in two locations: North American countries and Arabian Peninsula countries. Simple techniques for comparing individuals who have been completely vaccinated against COVID-19 have been applied, which may be used to generate the foundation for conclusions. Most significantly, a modern statistical model was created to present the best assessment of individuals completely vaccinated against COVID-19 data in nations in North America and the Arabian Peninsula. Some of the suggested statistical model features were proposed. Furthermore, the estimate of the model parameters was driven using the maximum likelihood estimation method. Results. The flexibility provided by the proposed statistical model is useful for describing the percentage of the individuals completely vaccinated against COVID-19, which provides a close fit with the COVID-19 data. Implications. The proposed statistical model can be used for statistics and generate new statistical distributions that can be used to compare and predict the process of people's willingness to vaccinate and take the vaccine to try to eliminate COVID-19.

Bayesian Analysis of Dynamic Cumulative Residual Entropy for Lindley Distribution

Dynamic cumulative residual (DCR) entropy is a valuable randomness metric that may be used in survival analysis. The Bayesian estimator of the DCR Rényi entropy (DCRRéE) for the Lindley distribution using the gamma prior is discussed in this article. Using a number of selective loss functions, the Bayesian estimator and the Bayesian credible interval are calculated. In order to compare the theoretical results, a Monte Carlo simulation experiment is proposed. Generally, we note that for a small true value of the DCRRéE, the Bayesian estimates under the linear exponential loss function are favorable compared to the others based on this simulation study. Furthermore, for large true values of the DCRRéE, the Bayesian estimate under the precautionary loss function is more suitable than the others. The Bayesian estimates of the DCRRéE work well when increasing the sample size. Real-world data is evaluated for further clarification, allowing the theoretical results to be validated.

The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data

In this article, the "truncated-composed" scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.

Estimation of different types of entropies for the Kumaraswamy distribution

The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided.

Discrimination of sunflower seeds using multispectral and texture dataset in combination with region selection and supervised classification methods

The purpose of this study is to discriminate sunflower seeds with the help of a dataset having spectral and textural features. The production of crop based on seed purity and quality other hand sunflower seed used for oil content worldwide. In this regard, the foundation of a dataset categorizes sunflower seed varieties (Syngenta CG, HS360, S278, HS30, Armani, and High Sun 33), which were acquired from the agricultural farms of The Islamia University of Bahawalpur, Pakistan, into six classes. For preprocessing, a new region-oriented seed-based segmentation was deployed for the automatic selection of regions and extraction of 53 multi-features from each region, while 11 optimized fused multi-features were selected using the chi-square feature selection technique. For discrimination, four supervised classifiers, namely, deep learning J4, support vector machine, random committee, and Bayes net, were employed to optimize the multi-feature dataset. We observe very promising accuracies of 98.2%, 97.5%, 96.6%, and 94.8%, respectively, when the size of a region is (180 × 180).

Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.

Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications

In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies…). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.

Truncated Inverted Kumaraswamy Generated Family of Distributions with Applications

In this article, we introduce a new general family of distributions derived to the truncated inverted Kumaraswamy distribution (on the unit interval), called the truncated inverted Kumaraswamy generated family. Among its qualities, it is characterized with tractable functions, has the ability to enhance the flexibility of a given distribution, and demonstrates nice statistical properties, including competitive fits for various kinds of data. A particular focus is given on a special member of the family defined with the exponential distribution as baseline, offering a new three-parameter lifetime distribution. This new distribution has the advantage of having a hazard rate function allowing monotonically increasing, decreasing, and upside-down bathtub shapes. In full generality, important properties of the new family are determined, with an emphasis on the entropy (Rényi and Shannon entropy). The estimation of the model parameters is established by the maximum likelihood method. A numerical simulation study illustrates the nice performance of the obtained estimates. Two practical data sets are then analyzed. We thus prove the potential of the new model in terms of fitting, with favorable results in comparison to other modern parametric models of the literature.