Different estimation methods of the modified Kies Topp-Leone model with applications and quantile regression.

This paper introduces the modified Kies Topp-Leone (MKTL) distribution for modeling data on the (0, 1) or [0, 1] interval. The shapes of the density and hazard rate functions manifest desirable shapes, making the MKTL distribution suitable for modeling data with different characteristics at the unit interval. Twelve different estimation methods are utilized to estimate the distribution parameters, and Monte Carlo simulation experiments are executed to assess the performance of the methods. The simulation results suggest that the maximum likelihood method is the superior method. The usefulness of the new distribution is illustrated by utilizing three data sets, and its performance is juxtaposed with that of other competing models. The findings affirm the superiority of the MKTL distribution over the other candidate models. Applying the developed quantile regression model using the new distribution disclosed that it offers a competitive fit over other existing regression models.

Construction of improved comprehensive classes of estimators for population distribution function.

The primary purpose of this article is to examine the issue of estimating the finite population distribution function from auxiliary information, such as population mean and rank of the auxiliary variables, that are already known. In order to better estimate the distribution function (DF) of a finite population, two improved estimators are developed. The bias and mean squared error of the suggested and existing estimators are derived up to the first order of approximation. To improve the efficiency of an estimators, we compare the suggested estimators with existing counterpart. Based on the numerical outcomes, it is to be noted that the suggested classes of estimators perform well using six actual data sets. The strength and generalization of the suggested estimators are also verified using a simulation analysis. Based on the result of actual data sets and a simulation study, we observe that the suggested estimator outperforms as compared to all existing estimators which is compared in this study.

Estimation methods based on ranked set sampling for the power logarithmic distribution.

The sample strategy employed in statistical parameter estimation issues has a major impact on the accuracy of the parameter estimates. Ranked set sampling (RSS) is a highly helpful technique for gathering data when it is difficult or impossible to quantify the units in a population. A bounded power logarithmic distribution (PLD) has been proposed recently, and it may be used to describe many real-world bounded data sets. In the current work, the three parameters of the PLD are estimated using the RSS technique. A number of conventional estimators using maximum likelihood, minimum spacing absolute log-distance, minimum spacing square distance, Anderson-Darling, minimum spacing absolute distance, maximum product of spacings, least squares, Cramer-von-Mises, minimum spacing square log distance, and minimum spacing Linex distance are investigated. The different estimates via RSS are compared with their simple random sampling (SRS) counterparts. We found that the maximum product spacing estimate appears to be the best option based on our simulation results for the SRS and RSS data sets. Estimates generated from SRS data sets are less efficient than those derived from RSS data sets. The usefulness of the RSS estimators is also investigated by means of a real data example.

The development of an extended Weibull model with applications to medicine, industry and actuarial sciences.

This paper delves into the theoretical and practical exploration of the complementary Bell Weibull (CBellW) model, which serves as an analogous counterpart to the complementary Poisson Weibull model. The study encompasses a comprehensive examination of various statistical properties of the CBellW model. Real data applications are carried out in three different fields, namely the medical, industrial and actuarial fields, to show the practical versatility of the CBellW model. For the medical data segment, the study utilizes four data sets, including information on daily confirmed COVID-19 cases and cancer data. Additionally, a Group Acceptance Sampling Plan (GASP) is designed by using the median as quality parameter. Furthermore, some actuarial risk measures for the CBellW model are obtained along with a numerical illustration of the Value at Risk and the Expected Shortfall. The research is substantiated by a comprehensive numerical analysis, model comparisons, and graphical illustrations that complement the theoretical foundation.

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 Xi. 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.

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 COVID-19 Data for Three Different Regions in the Kingdom of Saudi Arabia: Using a New Two-Parameter Statistical Model.

Since December 2019, the COVID-19 outbreak has touched every area of everyday life and caused immense destruction to the planet. More than 150 nations have been affected by the coronavirus outbreak. Many academics have attempted to create a statistical model that may be used to interpret the COVID-19 data. This article extends to probability theory by developing a unique two-parameter statistical distribution called the half-logistic inverse moment exponential (HLIMExp). Advanced mathematical characterizations of the suggested distribution have explicit formulations. The maximum likelihood estimation approach is used to provide estimates for unknown model parameters. A complete simulation study is carried out to evaluate the performance of these estimations. Three separate sets of COVID-19 data from Al Bahah, Al Madinah Al Munawarah, and Riyadh are utilized to test the HLIMExp model's applicability. The HLIMExp model is compared to several other well-known distributions. Using several analytical criteria, the results show that the HLIMExp distribution produces promising outcomes in terms of flexibility.

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).

The Truncated Cauchy Power Family of Distributions with Inference and Applications.

As a matter of fact, the statistical literature lacks of general family of distributions based on the truncated Cauchy distribution. In this paper, such a family is proposed, called the truncated Cauchy power-G family. It stands out for the originality of the involved functions, its overall simplicity and its desirable properties for modelling purposes. In particular, (i) only one parameter is added to the baseline distribution avoiding the over-parametrization phenomenon, (ii) the related probability functions (cumulative distribution, probability density, hazard rate, and quantile functions) have tractable expressions, and (iii) thanks to the combined action of the arctangent and power functions, the flexible properties of the baseline distribution (symmetry, skewness, kurtosis, etc.) can be really enhanced. These aspects are discussed in detail, with the support of comprehensive numerical and graphical results. Furthermore, important mathematical features of the new family are derived, such as the moments, skewness and kurtosis, two kinds of entropy and order statistics. For the applied side, new models can be created in view of fitting data sets with simple or complex structure. This last point is illustrated by the consideration of the Weibull distribution as baseline, the maximum likelihood method of estimation and two practical data sets wit different skewness properties. The obtained results show that the truncated Cauchy power-G family is very competitive in comparison to other well implanted general families.

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.

Estimation of Entropy for Inverse Lomax Distribution under Multiple Censored Data.

The inverse Lomax distribution has been widely used in many applied fields such as reliability, geophysics, economics and engineering sciences. In this paper, an unexplored practical problem involving the inverse Lomax distribution is investigated: the estimation of its entropy when multiple censored data are observed. To reach this goal, the entropy is defined through the Rényi and q-entropies, and we estimate them by combining the maximum likelihood and plugin methods. Then, numerical results are provided to show the behavior of the estimates at various sample sizes, with the determination of the mean squared errors, two-sided approximate confidence intervals and the corresponding average lengths. Our numerical investigations show that, when the sample size increases, the values of the mean squared errors and average lengths decrease. Also, when the censoring level decreases, the considered of Rényi and q-entropies estimates approach the true value. The obtained results validate the usefulness and efficiency of the method. An application to two real life data sets is given.