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.

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.

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。

Using Monte Carlo Simulation Technology to Improve Intuitive Effect of Teaching Probability and Mathematical Statistics Course

With the illustration of a specific problem, this paper demonstrates that using Monte Carlo Simulation technology will improve intuitive effect of teaching Probability and Mathematical Statistics course, and save instructors' effort as well.And it is estimated that Monte Carlo Simulation technology will be one of the major teaching methods for Probability and Mathematical Statistics course in the future.

The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation

The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.

A New Approach to Probability Theory with Reference to Statistics and Statistical Physics

A new approach to probability theory is presented with reference to statistics and statistical physics. At the outset, it is recognized that the “average man” of a population and the “average particle” of a gas are only objects of thought, and not real entities which exist in nature. The concept of average (man) is generalized as a new concept of represental (man) whose epistemological status is intermediate between those of the particular (the man) and the universal (a man). This new concept has become necessary as a result of emergence of statistics as a new branch of human knowledge at the beginning of the nineteenth century. Probability is defined with reference to the represental. The concept of probability is the same in probability theory and in physics. But whereas in statistics the probabilities are estimated using random sequences, in statistical physics they are determined either by the laws of physics alone or by making use of the laws of probability also. Thus in physics we deal with probability at a more basic level than in statistics. This approach is free from most of the controversies we face at present in interpreting probability theory and quantum mechanics.

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.

Probability Distribution Characteristics of Strong Nonlinear Waves Under Typhoon Conditions in the Northern South China Sea

The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.

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.

Probability Laws Derived from the Gamma Function

Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

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.

Stochastic Model of Dengue: Analysing the Probability of Extinction and LLN

In this article, we develop and analyze a continuous-time Markov chain (CTMC) model to study the resurgence of dengue. We also explore the large population asymptotic behavior of probabilistic model of dengue using the law of large numbers (LLN). Initially, we calculate and estimate the probabilities of dengue extinction and major outbreak occurrence using multi-type Galton-Watson branching processes. Subsequently, we apply the LLN to examine the convergence of the stochastic model towards the deterministic model. Finally, theoretical numerical simulations are conducted exploration to validate our findings. Under identical conditions, our numerical results demonstrate that dengue could vanish in the stochastic model while persisting in the deterministic model. The highlighting of the law of large numbers through numerical simulations indicates from what population size a deterministic model should be considered preferable.

High-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer based on probability density evolution method

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.

Integrating host biological and ecological variables to predict probability of haemosporidian infection in raptors

Variations in host traits that influence their exposure and susceptibility may impact probability of vector-transmitted diseases.Therefore,identifying the predictors of infection probability is necessary to understand the risk of disease outbreaks during expanding environmental perturbation.Here,we conducted a large survey based on microscopic examination and molecular analysis of haemosporidian parasite infection in raptors rescued at the Beijing Raptor Rescue Centre.Combining these data with biological and ecological variables of the raptors,we determined predictors that affect the probability of haemosporidian infection using generalized linear mixed models and multimodel inference.Our results showed that infection probability exhibited considerable variation across host species in raptors,and body mass,sex,and evolutionary history played relatively weaker roles in driving infection probability.Instead,activity pattern,age,geographic range size,migration distance,and nest type were important predictors of the probability of haemosporidian infection,and the role of each predictor differed in the three main haemosporidian genera(Plasmodium,Haemoproteus,and Leucocytozoon).This macro-ecological analysis will add to our understanding of host traits that influence the probability of avian haemosporidian infection and will help inform risk of emerging diseases.

Secrecy Outage Probability Minimization in Wireless-Powered Communications Using an Improved Biogeography-Based Optimization-Inspired Recurrent Neural Network

This paper focuses on wireless-powered communication systems,which are increasingly relevant in the Internet of Things(IoT)due to their ability to extend the operational lifetime of devices with limited energy.The main contribution of the paper is a novel approach to minimize the secrecy outage probability(SOP)in these systems.Minimizing SOP is crucial for maintaining the confidentiality and integrity of data,especially in situations where the transmission of sensitive data is critical.Our proposed method harnesses the power of an improved biogeography-based optimization(IBBO)to effectively train a recurrent neural network(RNN).The proposed IBBO introduces an innovative migration model.The core advantage of IBBO lies in its adeptness at maintaining equilibrium between exploration and exploitation.This is accomplished by integrating tactics such as advancing towards a random habitat,adopting the crossover operator from genetic algorithms(GA),and utilizing the global best(Gbest)operator from particle swarm optimization(PSO)into the IBBO framework.The IBBO demonstrates its efficacy by enabling the RNN to optimize the system parameters,resulting in significant outage probability reduction.Through comprehensive simulations,we showcase the superiority of the IBBO-RNN over existing approaches,highlighting its capability to achieve remarkable gains in SOP minimization.This paper compares nine methods for predicting outage probability in wireless-powered communications.The IBBO-RNN achieved the highest accuracy rate of 98.92%,showing a significant performance improvement.In contrast,the standard RNN recorded lower accuracy rates of 91.27%.The IBBO-RNN maintains lower SOP values across the entire signal-to-noise ratio(SNR)spectrum tested,suggesting that the method is highly effective at optimizing system parameters for improved secrecy even at lower SNRs.

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.

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.

A self-organization formation configuration based assignment probability and collision detection

The formation control of multiple unmanned aerial vehicles(multi-UAVs)has always been a research hotspot.Based on the straight line trajectory,a multi-UAVs target point assignment algorithm based on the assignment probability is proposed to achieve the shortest overall formation path of multi-UAVs with low complexity and reduce the energy consumption.In order to avoid the collision between UAVs in the formation process,the concept of safety ball is introduced,and the collision detection based on continuous motion of two time slots and the lane occupation detection after motion is proposed to avoid collision between UAVs.Based on the idea of game theory,a method of UAV motion form setting based on the maximization of interests is proposed,including the maximization of self-interest and the maximization of formation interest is proposed,so that multi-UAVs can complete the formation task quickly and reasonably with the linear trajectory assigned in advance.Finally,through simulation verification,the multi-UAVs target assignment algorithm based on the assignment probability proposed in this paper can effectively reduce the total path length,and the UAV motion selection method based on the maximization interests can effectively complete the task formation.