About 170 nations have been affected by the COvid VIrus Disease-19(COVID-19)epidemic.On governing bodies across the globe,a lot of stress is created by COVID-19 as there is a continuous rise in patient count testing p...About 170 nations have been affected by the COvid VIrus Disease-19(COVID-19)epidemic.On governing bodies across the globe,a lot of stress is created by COVID-19 as there is a continuous rise in patient count testing positive,and they feel challenging to tackle this situation.Most researchers concentrate on COVID-19 data analysis using the machine learning paradigm in these situations.In the previous works,Long Short-Term Memory(LSTM)was used to predict future COVID-19 cases.According to LSTM network data,the outbreak is expected tofinish by June 2020.However,there is a chance of an over-fitting problem in LSTM and true positive;it may not produce the required results.The COVID-19 dataset has lower accuracy and a higher error rate in the existing system.The proposed method has been introduced to overcome the above-mentioned issues.For COVID-19 prediction,a Linear Decreasing Inertia Weight-based Cat Swarm Optimization with Half Binomial Distribution based Convolutional Neural Network(LDIWCSO-HBDCNN)approach is presented.In this suggested research study,the COVID-19 predicting dataset is employed as an input,and the min-max normalization approach is employed to normalize it.Optimum features are selected using Linear Decreasing Inertia Weight-based Cat Swarm Optimization(LDIWCSO)algorithm,enhancing the accuracy of classification.The Cat Swarm Optimization(CSO)algorithm’s convergence is enhanced using inertia weight in the LDIWCSO algorithm.It is used to select the essential features using the bestfitness function values.For a specified time across India,death and confirmed cases are predicted using the Half Binomial Distribution based Convolutional Neural Network(HBDCNN)technique based on selected features.As demonstrated by empirical observations,the proposed system produces significant performance in terms of f-measure,recall,precision,and accuracy.展开更多
In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial (CAR-NB) model is employed to allow for overdispersion (tackl...In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial (CAR-NB) model is employed to allow for overdispersion (tackled by the NB component), unobserved heterogeneity and spatial autocorrelation (captured by the CAR process), using Markov chain Monte Carlo methods and the Gibbs sampler. Statistical tests suggest that the CAR-NB model is preferred over the CAR-Poisson, NB, zero-inflated Poisson, zero-inflated NB models, due to its lower prediction errors and more robust parameter inference. The study results show that crash frequency and fatalities are positively associated with the number of lanes, curve length, annual average daily traffic (AADT) per lane, as well as rainfall. Speed limit and the distances to the nearest hospitals have negative associations with segment-based crash counts but positive associations with fatality counts, presumably as a result of worsened collision impacts at higher speed and time loss during transporting crash victims.展开更多
In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the...In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer's arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.展开更多
The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximu...The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.展开更多
This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu...This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.展开更多
For the first time we derive the evolution law of the negative binomial state In) (nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state ...For the first time we derive the evolution law of the negative binomial state In) (nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.展开更多
In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. O...In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).展开更多
Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item sp...Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.展开更多
We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realiz...We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ(t) is totally determined by the parameters involved in the Hamiltonian.展开更多
In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design ...In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design the pricing formula for European option. Compared with the continuous situation, the proposed value equation of option under the new binomial tree model converges to Merton’s accurate analytical solution, and the established binomial tree method can be proved to work better than the traditional binomial tree. Finally, a numerical example is presented to illustrate the effectiveness of the proposed pricing methods.展开更多
The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random t...The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.展开更多
The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in ...The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in Appl.Math.Lett.23(2010)68-72 and Appl.Math.Comput.220(2013)482-486.展开更多
Quantum statistical properties of the binomial field interacting with the two entangled atoms are investi-gated for the different initial conditions.It is found that the sub-Poissonian distribution and the antibunchin...Quantum statistical properties of the binomial field interacting with the two entangled atoms are investi-gated for the different initial conditions.It is found that the sub-Poissonian distribution and the antibunching effect canbe presented for the certain ranges of the involved parameters.展开更多
文摘About 170 nations have been affected by the COvid VIrus Disease-19(COVID-19)epidemic.On governing bodies across the globe,a lot of stress is created by COVID-19 as there is a continuous rise in patient count testing positive,and they feel challenging to tackle this situation.Most researchers concentrate on COVID-19 data analysis using the machine learning paradigm in these situations.In the previous works,Long Short-Term Memory(LSTM)was used to predict future COVID-19 cases.According to LSTM network data,the outbreak is expected tofinish by June 2020.However,there is a chance of an over-fitting problem in LSTM and true positive;it may not produce the required results.The COVID-19 dataset has lower accuracy and a higher error rate in the existing system.The proposed method has been introduced to overcome the above-mentioned issues.For COVID-19 prediction,a Linear Decreasing Inertia Weight-based Cat Swarm Optimization with Half Binomial Distribution based Convolutional Neural Network(LDIWCSO-HBDCNN)approach is presented.In this suggested research study,the COVID-19 predicting dataset is employed as an input,and the min-max normalization approach is employed to normalize it.Optimum features are selected using Linear Decreasing Inertia Weight-based Cat Swarm Optimization(LDIWCSO)algorithm,enhancing the accuracy of classification.The Cat Swarm Optimization(CSO)algorithm’s convergence is enhanced using inertia weight in the LDIWCSO algorithm.It is used to select the essential features using the bestfitness function values.For a specified time across India,death and confirmed cases are predicted using the Half Binomial Distribution based Convolutional Neural Network(HBDCNN)technique based on selected features.As demonstrated by empirical observations,the proposed system produces significant performance in terms of f-measure,recall,precision,and accuracy.
基金The National Science Foundation by Changjiang Scholarship of Ministry of Education of China(No.BCS-0527508)the Joint Research Fund for Overseas Natural Science of China(No.51250110075)+1 种基金the Natural Science Foundation of Jiangsu Province(No.SBK200910046)the Postdoctoral Science Foundation of Jiangsu Province(No.0901005C)
文摘In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial (CAR-NB) model is employed to allow for overdispersion (tackled by the NB component), unobserved heterogeneity and spatial autocorrelation (captured by the CAR process), using Markov chain Monte Carlo methods and the Gibbs sampler. Statistical tests suggest that the CAR-NB model is preferred over the CAR-Poisson, NB, zero-inflated Poisson, zero-inflated NB models, due to its lower prediction errors and more robust parameter inference. The study results show that crash frequency and fatalities are positively associated with the number of lanes, curve length, annual average daily traffic (AADT) per lane, as well as rainfall. Speed limit and the distances to the nearest hospitals have negative associations with segment-based crash counts but positive associations with fatality counts, presumably as a result of worsened collision impacts at higher speed and time loss during transporting crash victims.
基金supported by the NSFC(11171101)Doctoral Fund of Education Ministry of China(20104306110001)the Graduate Research and Innovation Fund of Hunan Province(CX2011B197)
文摘In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer's arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.
基金supported by the National Natural Science Foundation of China(70471057)
文摘The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.
基金supported by the Nature Science Foundation of Hebei Province(A2014202202)supported by the Nature Science Foundation of China(11471218)
文摘This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 112470009)
文摘For the first time we derive the evolution law of the negative binomial state In) (nI in an ampli-tude dissipative channel with a damping constant to. We find that after passing through the channel, the final state is still a negative binomial state, however the parameter γ evolves into The decay law of theaverage photon number is also obtained.
基金The project supported by NNSFC (19631040), NSSFC (04BTJ002) and the grant for post-doctor fellows in SELF.
文摘In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).
文摘Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.
基金Project supported by the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2016AM03 and ZR2017MA011)
文摘We study how can an angular momentum coherent state |τ> keeps its form-invariant during time evolution governed by the Hamiltonian H = f(t)J++ f^*(t)J-+ g(t)Jz. We discuss this topic in the context of boson realization of |τ>. By employing the entangled state representation |ζ> and deriving a new binomial theorem involving two-subscript Hermite polynomials, we derive the wave function <ζ|τ>, which turns out to be a single-subscript Hermite polynomial. Based on this result the maintenance of angular momentum coherent state during time evolution is examined, and the value of τ(t) is totally determined by the parameters involved in the Hamiltonian.
文摘In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design the pricing formula for European option. Compared with the continuous situation, the proposed value equation of option under the new binomial tree model converges to Merton’s accurate analytical solution, and the established binomial tree method can be proved to work better than the traditional binomial tree. Finally, a numerical example is presented to illustrate the effectiveness of the proposed pricing methods.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61372156 and 61405053)the Natural Science Foundation of Zhejiang Province of China(Grant No.LZ13F04001)
文摘The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.
基金Supported by the Youth Backbone Teacher Foundation of Henan's University(Grant No.2016GGJS-117)Supported by the National Natural Science Foundation of China(Grant No.11871258)。
文摘The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in Appl.Math.Lett.23(2010)68-72 and Appl.Math.Comput.220(2013)482-486.
基金The project supported in part by the Science Foundation of China University of Petroleum under Grant No.Y061815
文摘Quantum statistical properties of the binomial field interacting with the two entangled atoms are investi-gated for the different initial conditions.It is found that the sub-Poissonian distribution and the antibunching effect canbe presented for the certain ranges of the involved parameters.