For evaluating reliability of an aviation pyrotechnics system,a Bayesian reliability estimation method utilizing reliability information of a system and its units was put forward. Firstly,an inheritance factor was det...For evaluating reliability of an aviation pyrotechnics system,a Bayesian reliability estimation method utilizing reliability information of a system and its units was put forward. Firstly,an inheritance factor was determined by chi-square goodness of fit test.Then the mixed prior distribution was obtained based on the inheritance factor. Finally, the density function of posterior distribution was obtained and used to assess the reliability of system.According to the new method, the reliability of an aviation pyrotechnics system was evaluated to reach 0. 989 6 at the confidence level of 0. 90. To reach the reliability index,the required numbers of trials of system and its units were given. It is instructional to apply the new method on the reliability estimation of aviation pyrotechnics systems.展开更多
Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization an...Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.展开更多
Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization an...Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.展开更多
With the gradual increase of distributed energy penetration,the traditional optimization model of distribution network can no longer guarantee the stable and efficient operation of the distribution network.In order to...With the gradual increase of distributed energy penetration,the traditional optimization model of distribution network can no longer guarantee the stable and efficient operation of the distribution network.In order to deal with the inevitable uncertainty of distributed energy,a new robust optimal operation method is proposed for active distribution network(ADN)based on the minimum confidence interval of distributed energy Beta distribution in this paper.First,an ADN model is established with second-order cone to include the energy storage device,capacitor bank,static var compensator,on-load tap changer,wind turbine and photovoltaic.Then,the historical data of related distributed energy are analyzed and described by the probability density function,and the minimum confidence interval is obtained by interval searching.Furthermore,via taking this minimum confidence interval as the uncertain interval,a less conservative two-stage robust optimization model is established and solved for ADN.The simulation results for the IEEE33-bus distribution network have verified that the proposed method can realize a more stable and efficient operation of the distribution network compared with the traditional robust optimization method.展开更多
On the basis of the Bayesian principle, a method of selecting the double beta distribution as a priori distribution is proposed for the system reliability evaluation when the available field test samples are small for...On the basis of the Bayesian principle, a method of selecting the double beta distribution as a priori distribution is proposed for the system reliability evaluation when the available field test samples are small for pyrotechnic device. Under the condition of different field and historical data, the mean square error(MSE) and coverage ratio(CR) of the reliability evaluation are compared by numerical simulation when the conjugate distribution and uniform distribution are selected as the priori distribution. Finally, the rationality and engineering applicability of the proposed method are verified through an example of the reliability evaluation of a typical pyrotechnic device.展开更多
Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Se...Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.展开更多
In this paper the density of the matrix variate beta distribution of rank lower than itsdimensionality is obtained with respect to a suitably defined differential form under the condi-tion that the difference between ...In this paper the density of the matrix variate beta distribution of rank lower than itsdimensionality is obtained with respect to a suitably defined differential form under the condi-tion that the difference between the identity and this matrix has full rank. As preliminaries,the Jacobian of a transformation related to decomposing a nonnegative-definite matrix into theproduct of a matrix of full column rank and its transpose and that of the transformation of anonnegative-definite matrix into its congruent matrix are established.展开更多
Avian wings are central to their remarkable flight ability and diverse life history strategies,including behaviors such as fighting and mating.These multifaceted functions are intricately tied to wing shape,which vari...Avian wings are central to their remarkable flight ability and diverse life history strategies,including behaviors such as fighting and mating.These multifaceted functions are intricately tied to wing shape,which varies significantly across species because of the complex interplay of evolutionary and ecological pressures.Many indices have been developed to quantify wing characteristics to facilitate the study and comparison of avian wing morphology across species.This study provides a comprehensive overview of existing quantitative methods for analyzing avian wing shapes.We then constructed a new quantification framework through the beta distribution,which can generate indices reflecting the shape of avian wings(center,dispersion,skewness,and kurtosis).Next,we used the flight feathers of 613 bird species to perform different quantitative analyses and explore the relationships between various wing shape quantification methods and life history traits,which serve as proxies for the selective forces shaping wing morphology.We find that the wing shape indices are more strongly associated with ecological variables than with morphological variables,especially for migration,habitat and territoriality.This research guides the selection of appropriate methods for wing shape analysis,contributing to a deeper understanding of avian morphology and its evolutionary drivers.展开更多
This paper derives a new decomposition of stock returns using price extremes and proposes a conditional autoregressive shape(CARS)model with beta density to predict the direction of stock returns.The CARS model is con...This paper derives a new decomposition of stock returns using price extremes and proposes a conditional autoregressive shape(CARS)model with beta density to predict the direction of stock returns.The CARS model is continuously valued,which makes it different from binary classification models.An empirical study is performed on the US stock market,and the results show that the predicting power of the CARS model is not only statistically significant but also economically valuable.We also compare the CARS model with the probit model,and the results demonstrate that the proposed CARS model outperforms the probit model for return direction forecasting.The CARS model provides a new framework for return direction forecasting.展开更多
In the reputation modeling of wireless sensor networks（WSNs） many literatures have proposed creative reputation indirect update methods,such as reputation integration,discounting,aging to eliminate,and filtering mal...In the reputation modeling of wireless sensor networks（WSNs） many literatures have proposed creative reputation indirect update methods,such as reputation integration,discounting,aging to eliminate,and filtering malicious reputation information. However,few have discussed the reputation direct update. In this paper,based on sound statistical theories,a negative binominal distribution method in the reputation direct update for WSNs is proposed. Results show that the proposed method is more suitable and time-saving for the reputation update of the resource constraint WSNs and can improve the computation power efficiency as well.展开更多
Tolerance analysis is investigated under an environment of concurrent design in order to lead to optimized tolerance, as traditional tolerance analysis is often inefficient and liable to mistakes. Making full use of k...Tolerance analysis is investigated under an environment of concurrent design in order to lead to optimized tolerance, as traditional tolerance analysis is often inefficient and liable to mistakes. Making full use of knowledge in manufacturing tolerance analysis combined with the beta distribution model is introduced and applied. The use of beta distribution reflects fully actual capabilities in manufacture. Concurrent tolerance design is a manufacturing environment oriented design process paying more attention to influences or restraints on product design caused by such factors as the manufacturing process, machine capabilities, economy in manufacturing, etc. Process environment oriented tolerance analysis is more flexible making the designed results more practical and effective.展开更多
A cued search algorithm with uncertain detection performance is proposed for phased array radars. Firstly, a target search model based on the information gain criterion is presented with known detection performance, a...A cued search algorithm with uncertain detection performance is proposed for phased array radars. Firstly, a target search model based on the information gain criterion is presented with known detection performance, and the statistical characteristic of the detection probability is calculated by using the fluctuant model of the target radar cross section （RCS）. Secondly, when the detection probability is completely unknown, its probability density function is modeled with a beta distribution, and its posterior probability distribution with the radar observation is derived based on the Bayesian theory. Finally simulation results show that the cued search algorithm with a known RCS fluctuant model can achieve the best performance, and the algorithm with the detection probability modeled as a beta distribution is better than that with a random selected detection probability because the model parameters can be updated by the radar observation to approach to the real value of the detection probability.展开更多
A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring t...A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring the differences between them,which might decrease the credibility level of reliability evaluation and result in data submergence.To solve the problem,a revised approach was derived to calculate groups of prior data's quantitative credibility,used for weighted data fusion.Then inheritance factor was introduced to build a mixed beta distribution to illustrate the innovation of new products.However,in many cases,inheritance factor was determined by Chi-square test that could not give out exact result with respect to rare failures.To make the model more precise,Barnard's exact test was suggested being used to calculate the inheritance factor.A numerical example is given to demonstrate that the modified method is successful and rational,while the classical method is too conservative and the traditional Bayesian method is too risky.展开更多
In this paper,a formal system is proposed based on beta reputation for the development of trustworthy wireless sensor networks(FRS-TWSN).Following this approach,key concepts related to reputation are formal described ...In this paper,a formal system is proposed based on beta reputation for the development of trustworthy wireless sensor networks(FRS-TWSN).Following this approach,key concepts related to reputation are formal described step by step for wireless sensor networks where sensor nodes maintain reputation for other sensors and use it to evaluate their trustworthiness.By proving some properties of beta reputation system,the beta distribution is founded to fit well to describe reputation system.Also,a case system is developed within this framework for reputation representation,updates and integration.Simulation results show this scheme not only can keep stable reputation but also can prevent the system from some attacks as bad mouthing and reputation cheating.展开更多
Acceptance sampling is a well-established statistical technique in quality assurance.Acceptance sampling is used to decide,acceptance or rejection of a lot based on the inspection of its random sample.Experts concur t...Acceptance sampling is a well-established statistical technique in quality assurance.Acceptance sampling is used to decide,acceptance or rejection of a lot based on the inspection of its random sample.Experts concur that the Bayesian approach is the best approach to make a correct decision,when historical knowledge is available.This paper suggests a Bayesian new group chain sampling plan(BNGChSP)to estimate average probability of acceptance.Binomial distribution function is used to differentiate between defective and non-defective products.Beta distribution is considered as a suitable prior distribution.Derivation is completed for the estimation of the average proportion of defectives.This study includes four quality regions namely:(i)probabilistic quality region(PQR),(ii)quality decision region(QDR),(iii)limiting quality region(LQR),and(iv)indifference quality region(IQR).The estimated values for the BNGChSPare tabulated and the inflection point values are derived,based on different combinations of design parameters including both consumer’s and producer’s risks.For comparison with the existing plan,the operating characteristic curves expose that BNGChSP is a better substitute for industrial practitioners.展开更多
Discrete epidemic models are applied to describe the physical phenomena of spreading infectious diseases in a household. In this paper, an attempt has been made to develop a modified epidemic chain model by assuming a...Discrete epidemic models are applied to describe the physical phenomena of spreading infectious diseases in a household. In this paper, an attempt has been made to develop a modified epidemic chain model by assuming a beta distribution of third kind for the probability of being infected by contact with a given infective from the same household with closed population. This paper emphasizes mainly on developing the probabilities of all possible epidemic chains with one introductory case for three, four and five member household. The key phenomenon towards developing this paper is to provide an alternative model of chain binomial model.展开更多
Under the assumption that asset prices follow a mixed gamma process,this paper first shows that return series can be presented as a difference of two gamma processes and then proposes a realized probability index for ...Under the assumption that asset prices follow a mixed gamma process,this paper first shows that return series can be presented as a difference of two gamma processes and then proposes a realized probability index for return direction forecasting.The underlying distribution of this new index is analyzed and found to be beta-distributed.Both theoretical and empirical results show that this new index is more efficient than the traditional binary index.展开更多
Four sites located in the north-eastern region of the United States of America have been chosen to investigate the impacts of soil heterogeneity in the transport of solutes(bromide and chloride)through the vadose zone...Four sites located in the north-eastern region of the United States of America have been chosen to investigate the impacts of soil heterogeneity in the transport of solutes(bromide and chloride)through the vadose zone(the zone in the soil that lies below the root zone and above the permanent saturated groundwater).A recently proposed mathematical model based on the cumulative beta distribution has been deployed to compare and contrast the regions'heterogeneity from multiple sample percolation experiments.Significant differences in patterns of solute leaching were observed even over a small spatial scale,indicating that traditional sampling methods for solute transport,for example the gravity pan or suction lysimeters,or more recent inventions such as the multiple sample percolation systems may not be effective in estimating solute fluxes in soils when a significant degree of soil heterogeneity is present.Consequently,ignoring soil heterogeneity in solute transport studies will likely result in under-or overprediction of leached fluxes and potentially lead to serious pollution of soils and/or groundwater.The cumulative beta distribution technique is found to be a versatile and simple technique of gaining valuable information regarding soil heterogeneity effects on solute transport.It is also an excellent tool for guiding future decisions of experimental designs particularly in regard to the number of samples within one site and the number of sampling locations between sites required to obtain a representative estimate of field solute or drainage flux.展开更多
Due to the usable frequency becomes more and more crowed, dynamic spectrum access （DSA） is a new hope to solve this problem. However, DSA in China requires a quantitative analysis of the current spectrum utilization...Due to the usable frequency becomes more and more crowed, dynamic spectrum access （DSA） is a new hope to solve this problem. However, DSA in China requires a quantitative analysis of the current spectrum utilization in frequency, temporal and spatial domains. In order to free the precious spectrum, spectrum regulation organizations must have a clear, detailed, up-to-date understanding of where, how and by whom spectrum is currently being used--such data is essential to sound policy decisions in the context of cognitive radio （CR）. In this paper, a concurrent spectrum occupancy measurement in south China was conducted to evaluate the practical spectrum occupancy with a digital wideband receiver covering from 20 MHz to 3 GHz. We also propose systemic spectrum measurement methodology, matrix format data storage, duty cycle （DC） evaluation metric and data mining process which can be a guideline for other researchers when they conduct the similar experiments. Quantitative analysis and characterization of the 4 different measurement locations are evaluated to promote the popularization of CR application in China. And a uniform Beta distribution channel occupancy model is also validated using real-scene measurement data. The experimental results demonstrate that there is a significant scope for license-exemption use of the released spectrum using CR technology.展开更多
Gene regulatory networks （GRNs） control the production of proteins in cells. It is well-known that this process is not deterministic. Numerous studies employed a non- deterministic transition structure to model thes...Gene regulatory networks （GRNs） control the production of proteins in cells. It is well-known that this process is not deterministic. Numerous studies employed a non- deterministic transition structure to model these networks. However, it is not realistic to expect state-to-state transition probabilities to remain constant throughout an organ- ism＇s lifetime. In this work, we focus on modeling GRN state transition （edge） variability using an ever-changing set of propensities. We suspect that the source of this variation is due to internal noise at the molecular level and can be modeled by introducing addi- tional stochasticity into GRN models. We employ a beta distribution, whose parameters are estimated to capture the pattern inherent in edge behavior with minimum error. Additionally, we develop a method for obtaining propensities from a pre-determined network.展开更多
基金Advanced Research Fund for National Defense Science and Technology Key Laboratory,China(No.9104C3705021003)
文摘For evaluating reliability of an aviation pyrotechnics system,a Bayesian reliability estimation method utilizing reliability information of a system and its units was put forward. Firstly,an inheritance factor was determined by chi-square goodness of fit test.Then the mixed prior distribution was obtained based on the inheritance factor. Finally, the density function of posterior distribution was obtained and used to assess the reliability of system.According to the new method, the reliability of an aviation pyrotechnics system was evaluated to reach 0. 989 6 at the confidence level of 0. 90. To reach the reliability index,the required numbers of trials of system and its units were given. It is instructional to apply the new method on the reliability estimation of aviation pyrotechnics systems.
文摘Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.
文摘Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.
基金supported in part by the National Natural Science Foundation of China(No.61703081)the Liaoning Joint Fund of National Natural Science Foundation of China(No.U1908217)+1 种基金the Natural Science Foundation of Liaoning Province(No.20170520113)the Fundamental Research Funds for the Central Universities(No.N2004016)。
文摘With the gradual increase of distributed energy penetration,the traditional optimization model of distribution network can no longer guarantee the stable and efficient operation of the distribution network.In order to deal with the inevitable uncertainty of distributed energy,a new robust optimal operation method is proposed for active distribution network(ADN)based on the minimum confidence interval of distributed energy Beta distribution in this paper.First,an ADN model is established with second-order cone to include the energy storage device,capacitor bank,static var compensator,on-load tap changer,wind turbine and photovoltaic.Then,the historical data of related distributed energy are analyzed and described by the probability density function,and the minimum confidence interval is obtained by interval searching.Furthermore,via taking this minimum confidence interval as the uncertain interval,a less conservative two-stage robust optimization model is established and solved for ADN.The simulation results for the IEEE33-bus distribution network have verified that the proposed method can realize a more stable and efficient operation of the distribution network compared with the traditional robust optimization method.
基金the National Natural Science Foundation of China(No.U1530135)
文摘On the basis of the Bayesian principle, a method of selecting the double beta distribution as a priori distribution is proposed for the system reliability evaluation when the available field test samples are small for pyrotechnic device. Under the condition of different field and historical data, the mean square error(MSE) and coverage ratio(CR) of the reliability evaluation are compared by numerical simulation when the conjugate distribution and uniform distribution are selected as the priori distribution. Finally, the rationality and engineering applicability of the proposed method are verified through an example of the reliability evaluation of a typical pyrotechnic device.
基金funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah under grant number(D-153-130-1441).The author,therefore,gratefully acknowledge the DSR technical and financial support.
文摘Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.
文摘In this paper the density of the matrix variate beta distribution of rank lower than itsdimensionality is obtained with respect to a suitably defined differential form under the condi-tion that the difference between the identity and this matrix has full rank. As preliminaries,the Jacobian of a transformation related to decomposing a nonnegative-definite matrix into theproduct of a matrix of full column rank and its transpose and that of the transformation of anonnegative-definite matrix into its congruent matrix are established.
基金supported by the National Natural Science Foundation of China(No.32170491)the Scientific Research Team Project of the College of Life Sciences,Beijing Normal University in 2024。
文摘Avian wings are central to their remarkable flight ability and diverse life history strategies,including behaviors such as fighting and mating.These multifaceted functions are intricately tied to wing shape,which varies significantly across species because of the complex interplay of evolutionary and ecological pressures.Many indices have been developed to quantify wing characteristics to facilitate the study and comparison of avian wing morphology across species.This study provides a comprehensive overview of existing quantitative methods for analyzing avian wing shapes.We then constructed a new quantification framework through the beta distribution,which can generate indices reflecting the shape of avian wings(center,dispersion,skewness,and kurtosis).Next,we used the flight feathers of 613 bird species to perform different quantitative analyses and explore the relationships between various wing shape quantification methods and life history traits,which serve as proxies for the selective forces shaping wing morphology.We find that the wing shape indices are more strongly associated with ecological variables than with morphological variables,especially for migration,habitat and territoriality.This research guides the selection of appropriate methods for wing shape analysis,contributing to a deeper understanding of avian morphology and its evolutionary drivers.
基金Funding was provided by National Social Science Fund of China(Grant No.22BJY259)National Natural Science Foundation of China(Grant Nos.71971004,72271055)Research on Modeling of Return Rate Based on Mixed Distribution and Its Application in Risk Management(Grant No.19YB26).
文摘This paper derives a new decomposition of stock returns using price extremes and proposes a conditional autoregressive shape(CARS)model with beta density to predict the direction of stock returns.The CARS model is continuously valued,which makes it different from binary classification models.An empirical study is performed on the US stock market,and the results show that the predicting power of the CARS model is not only statistically significant but also economically valuable.We also compare the CARS model with the probit model,and the results demonstrate that the proposed CARS model outperforms the probit model for return direction forecasting.The CARS model provides a new framework for return direction forecasting.
基金supported by the National Natural Science Foundation of China under Grant No. 6107311
文摘In the reputation modeling of wireless sensor networks（WSNs） many literatures have proposed creative reputation indirect update methods,such as reputation integration,discounting,aging to eliminate,and filtering malicious reputation information. However,few have discussed the reputation direct update. In this paper,based on sound statistical theories,a negative binominal distribution method in the reputation direct update for WSNs is proposed. Results show that the proposed method is more suitable and time-saving for the reputation update of the resource constraint WSNs and can improve the computation power efficiency as well.
文摘Tolerance analysis is investigated under an environment of concurrent design in order to lead to optimized tolerance, as traditional tolerance analysis is often inefficient and liable to mistakes. Making full use of knowledge in manufacturing tolerance analysis combined with the beta distribution model is introduced and applied. The use of beta distribution reflects fully actual capabilities in manufacture. Concurrent tolerance design is a manufacturing environment oriented design process paying more attention to influences or restraints on product design caused by such factors as the manufacturing process, machine capabilities, economy in manufacturing, etc. Process environment oriented tolerance analysis is more flexible making the designed results more practical and effective.
基金supported by the National Natural Science Foundation of China (61372165)the Postdoctoral Science Foundation of China (201150M15462012T50874)
文摘A cued search algorithm with uncertain detection performance is proposed for phased array radars. Firstly, a target search model based on the information gain criterion is presented with known detection performance, and the statistical characteristic of the detection probability is calculated by using the fluctuant model of the target radar cross section （RCS）. Secondly, when the detection probability is completely unknown, its probability density function is modeled with a beta distribution, and its posterior probability distribution with the radar observation is derived based on the Bayesian theory. Finally simulation results show that the cued search algorithm with a known RCS fluctuant model can achieve the best performance, and the algorithm with the detection probability modeled as a beta distribution is better than that with a random selected detection probability because the model parameters can be updated by the radar observation to approach to the real value of the detection probability.
基金National Natural Science Foundation of China(No.71371182)
文摘A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring the differences between them,which might decrease the credibility level of reliability evaluation and result in data submergence.To solve the problem,a revised approach was derived to calculate groups of prior data's quantitative credibility,used for weighted data fusion.Then inheritance factor was introduced to build a mixed beta distribution to illustrate the innovation of new products.However,in many cases,inheritance factor was determined by Chi-square test that could not give out exact result with respect to rare failures.To make the model more precise,Barnard's exact test was suggested being used to calculate the inheritance factor.A numerical example is given to demonstrate that the modified method is successful and rational,while the classical method is too conservative and the traditional Bayesian method is too risky.
基金the National Natural Science Foundation of China(60573043)the Natural Science Foundation of Guangdong Province(06025838)
文摘In this paper,a formal system is proposed based on beta reputation for the development of trustworthy wireless sensor networks(FRS-TWSN).Following this approach,key concepts related to reputation are formal described step by step for wireless sensor networks where sensor nodes maintain reputation for other sensors and use it to evaluate their trustworthiness.By proving some properties of beta reputation system,the beta distribution is founded to fit well to describe reputation system.Also,a case system is developed within this framework for reputation representation,updates and integration.Simulation results show this scheme not only can keep stable reputation but also can prevent the system from some attacks as bad mouthing and reputation cheating.
基金This research was supported by the Ministry of Education(MOE)through Fundamental Research Grant Scheme(FRGS/1/2020/STG06/UUM/02/2),S/O Code 14884.
文摘Acceptance sampling is a well-established statistical technique in quality assurance.Acceptance sampling is used to decide,acceptance or rejection of a lot based on the inspection of its random sample.Experts concur that the Bayesian approach is the best approach to make a correct decision,when historical knowledge is available.This paper suggests a Bayesian new group chain sampling plan(BNGChSP)to estimate average probability of acceptance.Binomial distribution function is used to differentiate between defective and non-defective products.Beta distribution is considered as a suitable prior distribution.Derivation is completed for the estimation of the average proportion of defectives.This study includes four quality regions namely:(i)probabilistic quality region(PQR),(ii)quality decision region(QDR),(iii)limiting quality region(LQR),and(iv)indifference quality region(IQR).The estimated values for the BNGChSPare tabulated and the inflection point values are derived,based on different combinations of design parameters including both consumer’s and producer’s risks.For comparison with the existing plan,the operating characteristic curves expose that BNGChSP is a better substitute for industrial practitioners.
文摘Discrete epidemic models are applied to describe the physical phenomena of spreading infectious diseases in a household. In this paper, an attempt has been made to develop a modified epidemic chain model by assuming a beta distribution of third kind for the probability of being infected by contact with a given infective from the same household with closed population. This paper emphasizes mainly on developing the probabilities of all possible epidemic chains with one introductory case for three, four and five member household. The key phenomenon towards developing this paper is to provide an alternative model of chain binomial model.
基金supported by the National Natural Science Foundation of China under Grant Nos.72271055 and 12201113。
文摘Under the assumption that asset prices follow a mixed gamma process,this paper first shows that return series can be presented as a difference of two gamma processes and then proposes a realized probability index for return direction forecasting.The underlying distribution of this new index is analyzed and found to be beta-distributed.Both theoretical and empirical results show that this new index is more efficient than the traditional binary index.
文摘Four sites located in the north-eastern region of the United States of America have been chosen to investigate the impacts of soil heterogeneity in the transport of solutes(bromide and chloride)through the vadose zone(the zone in the soil that lies below the root zone and above the permanent saturated groundwater).A recently proposed mathematical model based on the cumulative beta distribution has been deployed to compare and contrast the regions'heterogeneity from multiple sample percolation experiments.Significant differences in patterns of solute leaching were observed even over a small spatial scale,indicating that traditional sampling methods for solute transport,for example the gravity pan or suction lysimeters,or more recent inventions such as the multiple sample percolation systems may not be effective in estimating solute fluxes in soils when a significant degree of soil heterogeneity is present.Consequently,ignoring soil heterogeneity in solute transport studies will likely result in under-or overprediction of leached fluxes and potentially lead to serious pollution of soils and/or groundwater.The cumulative beta distribution technique is found to be a versatile and simple technique of gaining valuable information regarding soil heterogeneity effects on solute transport.It is also an excellent tool for guiding future decisions of experimental designs particularly in regard to the number of samples within one site and the number of sampling locations between sites required to obtain a representative estimate of field solute or drainage flux.
基金sponsored by the National Basic Research Program of China (2011CB302900)Postgraduate Innovation Fund of R&S-BUPT 2011+1 种基金National Key Technology R&D Program of China(2012ZX03003006)Shenzhen Bureau of Trade and Industry(JC200903170458A, JC201006010739A)
文摘Due to the usable frequency becomes more and more crowed, dynamic spectrum access （DSA） is a new hope to solve this problem. However, DSA in China requires a quantitative analysis of the current spectrum utilization in frequency, temporal and spatial domains. In order to free the precious spectrum, spectrum regulation organizations must have a clear, detailed, up-to-date understanding of where, how and by whom spectrum is currently being used--such data is essential to sound policy decisions in the context of cognitive radio （CR）. In this paper, a concurrent spectrum occupancy measurement in south China was conducted to evaluate the practical spectrum occupancy with a digital wideband receiver covering from 20 MHz to 3 GHz. We also propose systemic spectrum measurement methodology, matrix format data storage, duty cycle （DC） evaluation metric and data mining process which can be a guideline for other researchers when they conduct the similar experiments. Quantitative analysis and characterization of the 4 different measurement locations are evaluated to promote the popularization of CR application in China. And a uniform Beta distribution channel occupancy model is also validated using real-scene measurement data. The experimental results demonstrate that there is a significant scope for license-exemption use of the released spectrum using CR technology.
文摘Gene regulatory networks （GRNs） control the production of proteins in cells. It is well-known that this process is not deterministic. Numerous studies employed a non- deterministic transition structure to model these networks. However, it is not realistic to expect state-to-state transition probabilities to remain constant throughout an organ- ism＇s lifetime. In this work, we focus on modeling GRN state transition （edge） variability using an ever-changing set of propensities. We suspect that the source of this variation is due to internal noise at the molecular level and can be modeled by introducing addi- tional stochasticity into GRN models. We employ a beta distribution, whose parameters are estimated to capture the pattern inherent in edge behavior with minimum error. Additionally, we develop a method for obtaining propensities from a pre-determined network.
