Under classical statistics, research typically relies on precise data to estimate the population mean when auxiliary information is available. Outliers can pose a significant challenge in this process. The ultimate goal is to determine the most accurate estimates of the population mean while minimizing variance. Neutrosophic statistics is a generalization of classical statistics that deals with imprecise, uncertain data. Our research introduces the neutrosophic Hartley–Ross-type ratio estimators for estimating the population mean of neutrosophic data, even in the presence of outliers. We also incorporate neutrosophic versions of several robust regression methods, including LAD, Huber-M, Hampel-M, and Tukey-M. Our approach assumes that the study variable is both non-sensitive and sensitive, meaning that it can cause discomfort to participants during personal interviews, and measurement errors can occur due to dishonest responses. To address potential measurement errors, we propose the use of neutrosophic scrambling response models. Our proposed neutrosophic robust estimators are more effective than existing classical estimators, as confirmed by a computer-based numerical study using real data and simulation.

A social bot is an intelligent computer program that acts like a human and carries out various activities in a social network. A Twitter bot is one of the most common forms of social bots. The detection of Twitter bots has become imperative to draw lines between real and unreal Twitter users. In this research study, the main aim is to detect Twitter bots based on diverse content-specific feature sets and explore the use of state-of-the-art machine learning classifiers. The real-world data from Twitter is scrapped using Twitter API and is pre-processed using standard procedure. To analyze the content of tweets, several feature sets are proposed, such as message-based, part-of-speech, special characters, and sentiment-based feature sets. Min-max normalization is considered for data normalization and then feature selection methods are applied to rank the top features within each feature set. For empirical analysis, robust machine learning algorithms such as deep learning (DL), multilayer perceptron (MLP), random forest (RF), naïve Bayes (NB), and rule-based classification (RBC) are applied. The performance evaluation based on standard metrics of precision, accuracy, recall, and f-measure reveals that the proposed approach outperforms the existing studies in the relevant literature. In addition, we explore the effectiveness of each feature set for the detection of Twitter bots.

Several research investigations have stressed the importance of discrete data analysis and its relevance to actual events. The current work focuses on a new discrete distribution with a single parameter that can be derived using the Poisson mixing technique. The new distribution is named the Poisson Entropy-Based Weighted Exponential Distribution. It is useful for discussing asymmetric “right-skewed” data with “heavy” tails. Its failure rate function can be used to explain situations with increasing failure rates. The statistical properties of the new distribution are expressed explicitly. The proposed model is simple to manage for under-, equal-, and over-dispersed datasets. The model parameters are estimated using the maximum likelihood method. We consider the parameter estimation for the new model based on right-censored data with a cure fraction. One more focus of the present study is the Bayesian estimation of the model parameters. In the end, three real-world dataset examples were utilized to show the value of the new distribution. These applications revealed that the new model outperforms other standard discrete models.

Statistical modeling is a crucial phase for decision-making and predicting future events. Data arising from engineering-related fields have most often complex structures whose failure rate possesses mixed state behaviors (i.e., non-monotonic shapes). For the data sets whose failure rates are in the mixed state, the utilization of the traditional probability models is not a suitable choice. Therefore, searching for more flexible probability models that are capable of adequately describing the mixed state failure data sets is an interesting research topic for researchers. In this paper, we propose and study a new statistical model to achieve the above goal. The proposed model is called a new beta power very flexible Weibull distribution and is capable of capturing five different patterns of the failure rate such as uni-modal, decreasing-increasing-decreasing, bathtub, decreasing, increasing-decreasing-increasing shapes. The estimators of the new beta power very flexible Weibull distribution are obtained using the maximum likelihood method. The evaluation of the estimators is assessed by conducting a simulation study. Finally, the usefulness and applicability of the new beta power very flexible Weibull distribution are shown by analyzing two engineering data sets. Using four information criteria, it is observed that the new beta power very flexible Weibull distribution is the best-suited model for dealing with failure times data sets.

Fractional polytropic gas sphere problems and electrical engineering models typically simulated with interconnected circuits have numerous applications in physical, astrophysical phenomena, and thermionic currents. Generally, most of these models are singular-nonlinear, symmetric, and include time delay, which has increased attention to them among researchers. In this work, we explored deep neural networks (DNNs) with an optimization algorithm to calculate the approximate solutions for nonlinear fractional differential equations (NFDEs). The target data-driven design of the DNN-LM algorithm was further implemented on the fractional models to study the rigorous impact and symmetry of different parameters on RL, RC circuits, and polytropic gas spheres. The targeted data generated from the analytical and numerical approaches in the literature for different cases were utilized by the deep neural networks to predict the numerical solutions by minimizing the differences in mean square error using the Levenberg–Marquardt algorithm. The numerical solutions obtained by the designed technique were contrasted with the multi-step reproducing kernel Hilbert space method (MS-RKM), Laplace transformation method (LTM), and Padé approximations. The results demonstrate the accuracy of the design technique as the DNN-LM algorithm overlaps with the actual results with minimum percentage absolute errors that lie between 10${}^{-8}$ and 10${}^{-12}$. The extensive graphical and statistical analysis of the designed technique showed that the DNN-LM algorithm is dependable and facilitates the examination of higher-order nonlinear complex problems due to the flexibility of the DNN architecture and the effectiveness of the optimization procedure.

In this paper, we propose exponentiated XLindley (EXL) distribution. The novel model is adaptable due to the mixt shapes of its density and failure rate functions. The following key statistical properties of EXL distribution are derived: quantile function, moments, hazard function, mean residual life, and Rényi entropy. The parameters are estimated using the maximum likelihood, Anderson Darling, Cramer von Misses, maximum product spacing, ordinary and weighted least square estimation procedures. To examine the behavior of the estimate, Monte Carlo simulation is used. Further Bayesian technique is also utilized to estimate the EXL parameters. The traceplot and Geweke diagnostics are used to track the convergence of simulated processes. The applicability of the EXL distribution is demonstrated by three datasets from different domains such as mortality rate due to COVID-19, precipitation in inches, and failure time for repairable items. The proposed distribution provides efficient results as compared to renowned competitive distributions.