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In recent years, with the dramatic surge in the demand for health and elderly care services, the emergence of the health dividend has presented good development opportunities for health and wellness tourism. However, as a sector of the economy, health and wellness tourism still faces numerous challenges in achieving high-quality development. Therefore, this paper focuses on 31 provinces in China and constructs a multidimensional evaluation index system for the high-quality development of health and wellness tourism. The global entropy-weighted TOPSIS method and cluster analysis are used to conduct in-depth measurements, regional comparisons, and classification evaluations of the high-quality development of health and wellness tourism in each province. The research results indicate that: (1) From a quality perspective, the level of health and wellness tourism development in 11 provinces in China has exceeded the national average, while the remaining 20 provinces are below the national average. (2) From a regional perspective, the current level of high-quality development in health and wellness tourism decreases sequentially from the eastern to the central to the western regions, with significant regional differences. (3) Overall, the development in the 31 provinces can be categorized into five types: the High-Quality Benchmark Type, the High-Quality Stable Type, the High-Quality Progressive Type, the General-Quality Potential Type, and the General-Quality Lagging Type. (4) From a single-dimension analysis perspective, there are significant differences in the rankings of each province across different dimensions. Finally, this paper enriches and expands the theoretical foundation on the high-quality development of health and wellness tourism; on the other hand, it puts forward targeted countermeasures and suggestions to help promote the comprehensive enhancement of health and wellness tourism. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for the three-dimensional (3D) image visualization of objects under photon-starved conditions using multiple observations and statistical estimation. To visualize 3D objects under these conditions, photon counting integral imaging was used, which can extract photons from 3D objects using the Poisson random process. However, this process may not reconstruct 3D images under severely photon-starved conditions due to a lack of photons. Therefore, to solve this problem, in this paper, we propose N-observation photon-counting integral imaging with statistical estimation. Since photons are extracted randomly using the Poisson distribution, increasing the samples of photons can improve the accuracy of photon extraction. In addition, by using a statistical estimation method, such as maximum likelihood estimation, 3D images can be reconstructed. To prove our proposed method, we implemented the optical experiment and calculated its performance metrics, which included the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), peak-to-correlation energy (PCE), and the peak sidelobe ratio (PSR). [ABSTRACT FROM AUTHOR]

This study proposes a new five-parameter distribution called the gamma-exponentiated Weibull–Poisson (GEWP) distribution. As an extension of the exponentiated Weibull–Poisson family, the GEWP distribution offers a more flexible tool for analyzing a wider variety of data due to its theoretically and practically advantageous properties. It encompasses established distributions like the exponential, Weibull, and exponentiated Weibull. The development of the GEWP distribution proposed in this paper is obtained by combining the gamma–exponentiated Weibull (GEW) and the exponentiated Weibull–Poisson (EWP) distributions. Therefore, it serves as an extension of both the GEW and EWP distributions. This makes the GEWP a viable alternative for describing the variability of occurrences, enabling analysis in situations where GEW and EWP may be limited. This paper analyzes the probability distribution functions and provides the survival and hazard rate functions, the sub-models, the moments, the quantiles, and the maximum likelihood estimation of the GEWP distribution. Then, the numerical experiments for the parameter estimation of GEWP distribution for some finite sample sizes are presented. Finally, the comparative study of GEWP distribution and its sub-models is investigated via the goodness of fit test with real datasets to illustrate its potentiality. [ABSTRACT FROM AUTHOR]

Statistical data analysis is of great interest in every field of management, business, engineering, medicine, etc. At the time of classification and analysis, errors may arise, like a classification of observation in the other class instead of the actual class. All fields of science and economics have substantial problems due to misclassification errors in the observed data. Due to a misclassification error in the data, the sampling process may not suggest an appropriate probability distribution, and in that case, inference is impaired. When these types of errors are identified in variables, it is expected to consider the problem's solution regarding classification errors. This paper presents the situation where specific counts are reported erroneously as belonging to other counts in the context of size biased Uniform Poisson distribution, the so-called misclassified size biased Uniform Poisson distribution. Further, we have estimated the parameters of misclassified size biased Uniform Poisson distribution by applying the method of moments, maximum likelihood method, and approximate Bayes estimation method. A simulation study is carried out to assess the performance of estimation methods. A real dataset is discussed to demonstrate the suitability and applicability of the proposed distribution in the modeling count dataset. A Monte Carlo simulation study is presented to compare the estimators. The simulation results show that the ML estimates perform better than their corresponding moment estimates and approximate Bayes estimates. [ABSTRACT FROM AUTHOR]

In this paper, the stress–strength reliability $ R_{s,k} $ R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for $ R_{s,k} $ R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for $ R_{s,k} $ R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration. [ABSTRACT FROM AUTHOR]

This paper introduces a novel probability distribution known as the Ejaz distribution (ED), which is characterized by two parameters. The study offers a comprehensive analysis of this distribution, including an examination of key properties such as moments, moment-generating functions, order statistics, and reliability functions. Additionally, the paper explores the graphical representation of essential functions like the probability density function, cumulative distribution function, and hazard rate function, enhancing our visual understanding of their behavior. The distribution's parameters are estimated using the widely accepted method of maximum likelihood estimation. Through real-world examples, the paper highlights the practical applicability of the Ejaz distribution, demonstrating its performance and relevance in diverse scenarios. [ABSTRACT FROM AUTHOR]

This paper presents the exponentiated alpha-power log-logistic (EAPLL) distribution, which extends the log-logistic distribution. The EAPLL distribution emphasizes its suitability for survival data modeling by providing analytical simplicity and accommodating both monotone and non-monotone failure rates. We derive some of its mathematical properties and test eight estimation methods using an extensive simulation study. To determine the best estimation approach, we rank mean estimates, mean square errors, and average absolute biases on a partial and overall ranking. Furthermore, we use the EAPLL distribution to examine three real-life survival data sets, demonstrating its superior performance over competing log-logistic distributions. This study adds vital insights to survival analysis methodology and provides a solid framework for modeling various survival data scenarios. [ABSTRACT FROM AUTHOR]

Lattice Kalman filter (LKF) is a nonlinear Kalman filter that utilizes a deterministic sampling method with the advantages of optional sampling points and a flexible balance between computational burden and estimation accuracy. However, the fixed angle of sampling points in LKF can limit the optimality of the selected points. To this end, this paper proposes a novel maximum correntropy square-root rotating lattice Kalman filter (MCSRLKF) to improve the performance of LKF by adjusting the angle of sampling points. In MCSRLKF, a rotation matrix is first constructed to enhance the estimation accuracy of LKF and the optimal rotation angle of sampling points is selected to generate rotating lattice Kalman filter (RLKF). Then, the square-root RLKF (SRLKF) is proposed to enhance the stability and estimation accuracy of RLKF. Due to the utilization of the minimum mean square error criterion in SRLKF, there is a potential for significant performance degradation in non-Gaussian noises. Thus, to enhance the robustness against non-Gaussian noises, the maximum correntropy criterion is applied to SRLKF, generating MCSRLKF. Moreover, the Cramér-Rao lower bound (CRLB) serves as an indicator for assessing the performance of MCSRLKF. Finally, simulations on the nonlinear function model and reentry vehicle tracking model are used to demonstrate that MCSRLKF exhibits excellent filtering accuracy and robustness when dealing with non-Gaussian noises. [ABSTRACT FROM AUTHOR]

In this paper Chen-Burr XII distribution is constructed and graphical description of the probability density function, hazard rate and reversed hazard rate functions of the proposed model is obtained. Also, some statistical characteristics of the Chen-Burr XII distribution are discussed and some new models as sub-models from the Chen-Burr XII distribution are introduced. Moreover, maximum likelihood estimation of the parameters, reliability, hazard rate and reversed hazard rate functions of the Chen-Burr XII distribution are considered. Also, the asymptotic confidence intervals of the distribution parameters, reliability, hazard rate and reversed hazard rate functions are presented. Finally, three real life data sets are applied to prove how the Chen-Burr XII distribution can be applied in real life and to confirm its superiority over some existing distributions. [ABSTRACT FROM AUTHOR]

In this paper, we generalize two new statistical distributions, to improve the ability to model failure rates with non-monotonic, monotonic, and mainly bathtub curve behaviors. We call these distributions Generalized Powered Uniform Distribution and MOE-Powered Uniform. The proposed distributions' approach is based on incorporating a parameter k in the power of the values of the random variables, which is associated with the Probability Density Function and includes an operator called the Powered Mean. Various statistical and mathematical features focused on reliability analysis are presented and discussed, to make the models attractive to reliability engineering or medicine specialists. We employed the Maximum Likelihood Estimator method to estimate the model parameters and we analyzed its performance through a Monte Carlo simulation study. To demonstrate the flexibility of the proposed approach, a comparative analysis was carried out on four case studies with the proposed MOE-Powered Uniform distribution, which can model failure times as a bathtub curve. The results showed that this new model is more flexible and useful for performing reliability analysis. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a novel probability distribution model known as the unit compound Rayleigh distribution, which possesses the distinctive characteristic of defining the range within the bounded interval (0,1). Through an in-depth investigation of this distribution, we analyzed various statistical and structural characteristics including reliability function, risk function, quantile function, moment analysis, order statistics, and entropy measurement. To estimate the unknown parameters of our proposed distribution model, we employed maximum likelihood (ML) estimation and Bayesian estimation. Furthermore, we derived several entropy measures based on ML estimation under the unit compound Rayleigh distribution. To comprehensively evaluate the performance of these entropies, we employed the Monte Carlo simulation method to calculate the average entropy estimate, average entropy bias, corresponding mean square error, and mean relative estimate for assessing the performance of various entropies within the unit compound Rayleigh distribution model. Finally, in order to validate its potential for practical applications, two sets of real data were selected for empirical analysis where fitting and parameter estimation were conducted to demonstrate the advantages of utilizing the unit compound Rayleigh distribution in describing and predicting actual data. This study not only introduces a new probability theory and statistics framework by proposing a novel distribution model but also provides researchers and practitioners in related fields with a powerful analytical tool. [ABSTRACT FROM AUTHOR]