Lottery Numbers and Ordered Statistics

The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typically random and unpredictable. Some people use the lottery terminal randomly generates numbers for them, some players choose numbers that hold personal significance to them, such as birthdays, anniversaries, or other important dates, some enthusiasts have turned to statistical analysis as a means to analyze past winning numbers identify patterns or frequencies. In this paper, we use order statistics to estimate the probability of specific order of numbers or number combinations being drawn in future drawings.

Efficient ECG classification based on Chi-square distance for arrhythmia detection

This study introduces a new classifier tailored to address the limitations inherent in conventional classifiers such as K-nearest neighbor(KNN),random forest(RF),decision tree(DT),and support vector machine(SVM)for arrhythmia detection.The proposed classifier leverages the Chi-square distance as a primary metric,providing a specialized and original approach for precise arrhythmia detection.To optimize feature selection and refine the classifier’s performance,particle swarm optimization(PSO)is integrated with the Chi-square distance as a fitness function.This synergistic integration enhances the classifier’s capabilities,resulting in a substantial improvement in accuracy for arrhythmia detection.Experimental results demonstrate the efficacy of the proposed method,achieving a noteworthy accuracy rate of 98% with PSO,higher than 89% achieved without any previous optimization.The classifier outperforms machine learning(ML)and deep learning(DL)techniques,underscoring its reliability and superiority in the realm of arrhythmia classification.The promising results render it an effective method to support both academic and medical communities,offering an advanced and precise solution for arrhythmia detection in electrocardiogram(ECG)data.

Effect Evaluation of CBL Combined with Rain Classroom Teaching Method in Medical Statistics

Objective: To explore the application effect of CBL combined with rain classroom teaching method in medical statistics courses. Methods: The undergraduate students of medical imaging technology in 2019 and 2020 in a university were selected as the research objects. A cluster sampling method was used to select 79 undergraduate students from 2019 in the control group and 75 undergraduate students from 2020 in the experimental group. Traditional teaching method and CBL combined with rain classroom teaching method was used in the control group and experimental group respectively. The final examination scores of the two groups were compared. In experimental group, the correlation between the average score in the rain classroom and the final examination score was tested, and the teaching effect was evaluated. Results: The average score of final examination in experimental group and control group was 79.13 ± 10.32 points and 71.54 ± 14.752 points, respectively, which had a statistically significant difference (Z = 2.586, P = 0.012);the final examination scores of the students in the experimental group were positively correlated with the average scores of the rain classroom (r = 0.372, P = 0.001), and the proportion of satisfaction in the experimental group was 94.7%. Conclusion: The CBL combined with rain classroom teaching method can improve the teaching effectiveness of medical statistics courses.

Innovations and Challenges in Economic Census Methodology:A Study by the Bureau of Statistics

The Bureau of Statistics has demonstrated a forward-looking strategic approach in its economic census.By leveraging dual innovations in technology and management,and incorporating modern technologies such as big data,cloud computing,and the Internet of Things,it has deepened the reform of the census methodology.Additionally,the Bureau has built a multi-dimensional collaborative network that enhances international cooperation,departmental coordination,and public participation.This approach not only addresses the limitations of traditional statistical methods in a complex economic environment but also improves data quality and census efficiency,providing an accurate and reliable foundation for national economic decision-making.

Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course:A Teaching Design Based on Estimation and Hypothesis Testing

With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.

Research on the Application of PBL+SPOC Blended Teaching Model in Probability and Statistics Course

To cultivate talents with an exploratory spirit and practical skills in the era of information technology,it is imperative to reform teaching methods and approaches.In the teaching process of the Probability and Statistics course,an application-oriented blended teaching model combining problem-based learning and small private online course was explored.By organizing and implementing online and offline teaching activities based on problem-based learning,a multidimensional process-oriented learning assessment system was established.Practice has shown that this model can effectively enhance classroom teaching effectiveness,benefiting the improvement of students’overall skills and mathematical literacy.

留学生Medical Statistics线上课程建设与远程教学的实践与思考

受政治、经济和全球健康等因素影响,远程教育成为高等教育的一个发展趋势。新冠疫情防控期间,受出入境限制,未能返华的留学生一直以远程教学推进学业,成为其间持续进行远程教学最久的群体。本研究总结临床专业本科留学生主干课程Medical Statistics的校级一流线上课程建设与教学实践,并比较了疫情前后,线下教学与远程教学的留学生期末考试成绩,发现远程教学成绩经历波动后逐渐稳定并接近传统线下教学。本文同时对效果影响因素进行了调研和分析,发现“充分学习和使用远程课程中丰富的资源”和“上网是否容易”是留学生学习效果的主要影响因素。提出建设丰富教学资源对促进医学统计学远程学习效果的重要影响,同时提出对策建议,以期进一步提高远程教学水平,服务高校现代化课程体系建设。

Visualising data distributions with kernel density estimation and reduced chi-squared statistic

The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.

Chi-Square and PCA Based Feature Selection for Diabetes Detection with Ensemble Classifier

Diabetes mellitus is a metabolic disease that is ranked among the top 10 causes of death by the world health organization.During the last few years,an alarming increase is observed worldwide with a 70%rise in the disease since 2000 and an 80%rise in male deaths.If untreated,it results in complications of many vital organs of the human body which may lead to fatality.Early detection of diabetes is a task of significant importance to start timely treatment.This study introduces a methodology for the classification of diabetic and normal people using an ensemble machine learning model and feature fusion of Chi-square and principal component analysis.An ensemble model,logistic tree classifier(LTC),is proposed which incorporates logistic regression and extra tree classifier through a soft voting mechanism.Experiments are also performed using several well-known machine learning algorithms to analyze their performance including logistic regression,extra tree classifier,AdaBoost,Gaussian naive Bayes,decision tree,random forest,and k nearest neighbor.In addition,several experiments are carried out using principal component analysis(PCA)and Chi-square(Chi-2)fea-tures to analyze the influence of feature selection on the performance of machine learning classifiers.Results indicate that Chi-2 features show high performance than both PCA features and original features.However,the highest accuracy is obtained when the proposed ensemble model LTC is used with the proposed fea-ture fusion framework-work which achieves a 0.85 accuracy score which is the highest of the available approaches for diabetes prediction.In addition,the statis-tical T-test proves the statistical significance of the proposed approach over other approaches.

Removal of Stripes in Remote Sensing Images Based on Statistics Combined with Image Enhancement

A method to remove stripes from remote sensing images is proposed based on statistics and a new image enhancement method.The overall processing steps for improving the quality of remote sensing images are introduced to provide a general baseline.Due to the differences in satellite sensors when producing images,subtle but inherent stripes can appear at the stitching positions between the sensors.These stitchingstripes cannot be eliminated by conventional relative radiometric calibration.The inherent stitching stripes cause difficulties in downstream tasks such as the segmentation,classification and interpretation of remote sensing images.Therefore,a method to remove the stripes based on statistics and a new image enhancement approach are proposed in this paper.First,the inconsistency in grayscales around stripes is eliminated with the statistical method.Second,the pixels within stripes are weighted and averaged based on updated pixel values to enhance the uniformity of the overall image radiation quality.Finally,the details of the images are highlighted by a new image enhancement method,which makes the whole image clearer.Comprehensive experiments are performed,and the results indicate that the proposed method outperforms the baseline approach in terms of visual quality and radiation correction accuracy.

The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences

In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.

Enhancing Network Design through Statistical Evaluation of MANET Routing Protocols

This paper contributes a sophisticated statistical method for the assessment of performance in routing protocols salient Mobile Ad Hoc Network(MANET)routing protocols:Destination Sequenced Distance Vector(DSDV),Ad hoc On-Demand Distance Vector(AODV),Dynamic Source Routing(DSR),and Zone Routing Protocol(ZRP).In this paper,the evaluation will be carried out using complete sets of statistical tests such as Kruskal-Wallis,Mann-Whitney,and Friedman.It articulates a systematic evaluation of how the performance of the previous protocols varies with the number of nodes and the mobility patterns.The study is premised upon the Quality of Service(QoS)metrics of throughput,packet delivery ratio,and end-to-end delay to gain an adequate understanding of the operational efficiency of each protocol under different network scenarios.The findings explained significant differences in the performance of different routing protocols;as a result,decisions for the selection and optimization of routing protocols can be taken effectively according to different network requirements.This paper is a step forward in the general understanding of the routing dynamics of MANETs and contributes significantly to the strategic deployment of robust and efficient network infrastructures.

On power series statistical convergence and new uniform integrability of double sequences

In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

Evaluation of Serum Anti-Müllerian Hormone (AMH) Values for 28,016 Bulgarian Women: Prognostic Statistical Model of Age Specific AMH Declining

The present study aims to establish a relationship between serum AMH levels and age in a large group of women living in Bulgaria, as well as to establish reference age-specific AMH levels in women that would serve as an initial estimate of ovarian age. A total of 28,016 women on the territory of the Republic of Bulgaria were tested for serum AMH levels with a median age of 37.0 years (interquartile range 32.0 to 41.0). For women aged 20 - 29 years, the Bulgarian population has relatively high median levels of AMH, similar to women of Asian origin. For women aged 30 - 34 years, our results are comparable to those of women living in Western Europe. For women aged 35 - 39 years, our results are comparable to those of women living in the territory of India and Kenya. For women aged 40 - 44 years, our results were lower than those for women from the Western European and Chinese populations, close to the Indian and higher than Korean and Kenya populations, respectively. Our results for women of Bulgarian origin are also comparable to US Latina women at age 30, 35 and 40 ages. On the base on constructed a statistical model to predicting the decline in AMH levels at different ages, we found non-linear structure of AMH decline for the low AMH 3.5) the dependence of the decline of AMH on age was confirmed as linear. In conclusion, we evaluated the serum level of AMH in Bulgarian women and established age-specific AMH percentile reference values based on a large representative sample. We have developed a prognostic statistical model that can facilitate the application of AMH in clinical practice and the prediction of reproductive capacity and population health.

Statistical properties of ideal photons in a two-dimensional dye-filled spherical cap cavity

Within the framework of quantum statistical mechanics,we have proposed an exact analytical solution to the problemof Bose-Einstein condensation(BEC)of harmonically trapped two-dimensional(2D)ideal photons.We utilize this analyticalsolution to investigate the statistical properties of ideal photons in a 2D dye-filled spherical cap cavity.The resultsof numerical calculation of the analytical solution agree completely with the foregoing experimental results in the BEC ofharmonically trapped 2D ideal photons.The analytical expressions of the critical temperature and the condensate fractionare derived in the thermodynamic limit.It is found that the 2D critical photon number is larger than the one-dimensional(1D)critical photon number by two orders of magnitude.The spectral radiance of a 2D spherical cap cavity has a sharppeak at the frequency of the cavity cutoff when the photon number exceeds the critical value determined by a temperature.

Failure evolution and disaster prediction of rock under uniaxial compression based on non-extensive statistical analysis of electric potential

Rock failure can cause serious geological disasters,and the non-extensive statistical features of electric potential(EP)are expected to provide valuable information for disaster prediction.In this paper,the uniaxial compression experiments with EP monitoring were carried out on fine sandstone,marble and granite samples under four displacement rates.The Tsallis entropy q value of EPs is used to analyze the selforganization evolution of rock failure.Then the influence of displacement rate and rock type on q value are explored by mineral structure and fracture modes.A self-organized critical prediction method with q value is proposed.The results show that the probability density function(PDF)of EPs follows the q-Gaussian distribution.The displacement rate is positively correlated with q value.With the displacement rate increasing,the fracture mode changes,the damage degree intensifies,and the microcrack network becomes denser.The influence of rock type on q value is related to the burst intensity of energy release and the crack fracture mode.The q value of EPs can be used as an effective prediction index for rock failure like b value of acoustic emission(AE).The results provide useful reference and method for the monitoring and early warning of geological disasters.

Rapid Prediction of Wastewater Index Using CNN Architecture and PLS Series Statistical Methods

Chemical oxygen demand (COD) is an important index to measure the degree of water pollution. In this paper, near-infrared technology is used to obtain 148 wastewater spectra to predict the COD value in wastewater. First, the partial least squares regression (PLS) model was used as the basic model. Monte Carlo cross-validation (MCCV) was used to select 25 samples out of 148 samples that did not conform to conventional statistics. Then, the interval partial least squares (iPLS) regression modeling was carried out on 123 samples, and the spectral bands were divided into 40 subintervals. The optimal subintervals are 20 and 26, and the optimal correlation coefficient of the test set (RT) is 0.58. Further, the waveband is divided into five intervals: 17, 19, 20, 22 and 26. When the number of joint intervals under each interval is three, the optimal RT is 0.71. When the number of joint subintervals is four, the optimal RT is 0.79. Finally, convolutional neural network (CNN) was used for quantitative prediction, and RT was 0.9. The results show that CNN can automatically screen the features inside the data, and the quantitative prediction effect is better than that of iPLS and synergy interval partial least squares model (SiPLS) with joint subinterval three and four, indicating that CNN can be used for quantitative analysis of water pollution degree.

Integration between Genomic and Computational Statistical Surveys for the Screening of SNP Genetic Variants in Inflammatory Bowel Disease (IBD) Pediatric Patients*

Inflammatory bowel diseases (IBD) are complex multifactorial disorders that include Crohn’s disease (CD) and ulcerative colitis (UC). Considering that IBD is a genetic and multifactorial disease, we screened for the distribution dynamism of IBD pathogenic genetic variants (single nucleotide polymorphisms;SNPs) and risk factors in four (4) IBD pediatric patients, by integrating both clinical exome sequencing and computational statistical approaches, aiming to categorize IBD patients in CD and UC phenotype. To this end, we first aligned genomic read sequences of these IBD patients to hg19 human genome by using bowtie 2 package. Next, we performed genetic variant calling analysis in terms of single nucleotide polymorphism (SNP) for genes covered by at least 20 read genomic sequences. Finally, we checked for biological and genomic functions of genes exhibiting statistically significant genetic variant (SNPs) by introducing Fitcon genomic parameter. Findings showed Fitcon parameter as normalizing IBD patient’s population variability, as well as inducing a relative good clustering between IBD patients in terms of CD and UC phenotypes. Genomic analysis revealed a random distribution of risk factors and as well pathogenic SNPs genetic variants in the four IBD patient’s genome, claiming to be involved in: i) Metabolic disorders, ii) Autoimmune deficiencies;iii) Crohn’s disease pathways. Integration of genomic and computational statistical analysis supported a relative genetic variability regarding IBD patient population by processing IBD pathogenic SNP genetic variants as opposite to IBD risk factor variants. Interestingly, findings clearly allowed categorizing IBD patients in CD and UC phenotypes by applying Fitcon parameter in selecting IBD pathogenic genetic variants. Considering as a whole, the study suggested the efficiency of integrating clinical exome sequencing and computational statistical tools as a right approach in discriminating IBD phenotypes as well as improving inflammatory bowel disease (IBD) molecular diagnostic process.

Smart Healthcare Activity Recognition Using Statistical Regression and Intelligent Learning

In this present time,Human Activity Recognition(HAR)has been of considerable aid in the case of health monitoring and recovery.The exploitation of machine learning with an intelligent agent in the area of health informatics gathered using HAR augments the decision-making quality and significance.Although many research works conducted on Smart Healthcare Monitoring,there remain a certain number of pitfalls such as time,overhead,and falsification involved during analysis.Therefore,this paper proposes a Statistical Partial Regression and Support Vector Intelligent Agent Learning(SPR-SVIAL)for Smart Healthcare Monitoring.At first,the Statistical Partial Regression Feature Extraction model is used for data preprocessing along with the dimensionality-reduced features extraction process.Here,the input dataset the continuous beat-to-beat heart data,triaxial accelerometer data,and psychological characteristics were acquired from IoT wearable devices.To attain highly accurate Smart Healthcare Monitoring with less time,Partial Least Square helps extract the dimensionality-reduced features.After that,with these resulting features,SVIAL is proposed for Smart Healthcare Monitoring with the help of Machine Learning and Intelligent Agents to minimize both analysis falsification and overhead.Experimental evaluation is carried out for factors such as time,overhead,and false positive rate accuracy concerning several instances.The quantitatively analyzed results indicate the better performance of our proposed SPR-SVIAL method when compared with two state-of-the-art methods.

Generalized Kumaraswamy Generalized Power Gompertz Distribution: Statistical Properties, Application, and Validation Using a Modified Chi-Squared Goodness of Fit Test

A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function and cumulative distribution function is presented. The statistical features of the Generalized Kumaraswamy Generalized Power Gompertz distribution are systematically derived and adequately studied. The estimation of the model parameters in the absence of censoring and under-right censoring is performed using the method of maximum likelihood. The test statistic for right-censored data, criteria test for GKGPG distribution, estimated matrix Ŵ, Ĉ, and Ĝ, criteria test Y2n, alongside the quadratic form of the test statistic is derived. Mean simulated values of maximum likelihood estimates and their corresponding square mean errors are presented and confirmed to agree closely with the true parameter values. Simulated levels of significance for Y2n (γ) test for the GKGPG model against their theoretical values were recorded. We conclude that the null hypothesis for which simulated samples are fitted by GKGPG distribution is widely validated for the different levels of significance considered. From the summary of the results of the strength of a specific type of braided cord dataset on the GKGPG model, it is observed that the proposed GKGPG model fits the data set for a significance level ε = 0.05.