Covid-19 Forecasting with Deep Learning-based Half-binomial Distribution Cat Swarm Optimization

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.

Quasi-Binomial Regression Model for the Analysis of Data with Extra-Binomial Variation

Objectives: Developing inference procedures on the quasi-binomial distribution and the regression model. Methods: Score testing and the method of maximum likelihood for regression parameters estimation. Data: Several examples are included, based on published data. Results: A quasi-binomial model is used to model binary response data which exhibit extra-binomial variation. A partial score test on the binomial hypothesis versus the quasi-binomial alternative is developed and illustrated on three data sets. The extended logit transformation on the binomial parameter is introduced and the large sample dispersion matrix of the estimated parameters is derived. The Nonlinear Mixed Procedure (NLMIXED) in SAS is shown to be very appropriate for the estimation of nonlinear regression.

Log-binomial回归在社区干预效果评价中的应用

目的介绍利用log-binomial回归评价社区干预效果的原理与方法。方法通过在log-binomial模型中增加干预变量和时间变量的交互项,获得相对率比(RRR)的估计值,来进行社区干预效果评价,并以实例进行分析。结果通过"儿童关爱"干预措施对婴幼儿腹泻患病率影响的实例分析了在有无协变量的log-binomial回归在社区干预效果评价中的应用效果,并与Poisson回归模型做了相应的比较。调整混杂因子后的log-binomial回归模型是在控制了个体因素后对干预效应的有效估计,因此,评价的结果更为可靠。结论 log-binomial回归模型是社区干预研究的一种有效方法。

结合降维思想的BinomialBoosting方法

文章利用充分降维的思想,对分类问题的BinomialBoosting(BBoosting)算法进行了改进,提出了一种新的方法——Dimension Reduction BinomialBoosting(DRBBoosting)。这种算法在每次迭代中,结合充分降维方法,充分提取X与Y之间的信息,得到X的线性组合βTX,用βTX进行boosting迭代,避免了BBoosting对所有变量逐个分析。与BBoosting相比,收敛速度快,预测精度高;模拟比较也表明了DRBBoosting的优点。

On the Markov Chain Binomial Model

Rudolfer [1] studied properties and estimation of a state Markov chain binomial (MCB) model of extra-binomial variation. The variance expression in Lemma 4 is stated without proof but is incorrect, resulting in both Lemma 5 and Theorem 2 also being incorrect. These errors were corrected in Rudolfer [2]. In Sections 2 and 3 of this paper, a new derivation of the variance expression in a setting involving the natural parameters ?is presented and the relation of the MCB model to Edwards’ [3] probability generating function (pgf) approach is discussed. Section 4 deals with estimation of the model parameters. Estimation by the maximum likelihood method is difficult for a larger number n of Markov trials due to the complexity of the calculation of probabilities using Equation (3.2) of Rudolfer [1]. In this section, the exact maximum likelihood estimation of model parameters is obtained utilizing a sequence of Markov trials each involving n observations from a {0,1}-?state MCB model and may be used for any value of n. Two examples in Section 5 illustrate the usefulness of the MCB model. The first example gives corrected results for Skellam’s Brassica data while the second applies the “sequence approach” to data from Crouchley and Pickles [4].

Stochastic Orders Comparisons of Negative Binomial Distribution with Negative Binomial—Lindley Distribution

The purpose of this study is to compare a negative binomial distribution with a negative binomial—Lindley by using stochastic orders. We characterize the comparisons in usual stochastic order, likelihood ratio order, convex order, expectation order and uniformly more variable order based on theorem and some numerical example of comparisons between negative binomial random variable and negative binomial—Lindley random variable.

Statistical analysis of generalized exponential distribution under progressive censoring with binomial removals

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.

EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

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.

Evolution law of a negative binomial state in an amplitude dissipative channel

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.

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

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.

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

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)).

Time evolution of angular momentum coherent state derived by virtue of entangled state representation and a new binomial theorem

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.

The Series of Reciprocals of Non-central Binomial Coefficients

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.

Modeling random telegraph signal noise in CMOS image sensor under low light based on binomial distribution

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.

A New Binomial Tree Method for European Options under the Jump Diffusion Model

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.

基于Beta-Negative Binomial的膨胀分布推广及应用——以新冠病毒肺炎感染人数为例

新型冠状病毒肺炎现存确诊人数是评估疫情发展形势的重要指标,精确刻画新冠病毒肺炎现存确诊人数的分布对于我国开展疫情防治工作具有重要意义.以2021年1月1日~6日我国34个地区新冠病毒肺炎现存确诊人数为研究对象,构建现存确诊人数Beta-Negative Binomial分布、0膨胀Beta-Negative Binomial分布和0-1膨胀Beta-Negative Binomial分布,通过EM算法给出参数的点估计,并基于Fisher信息矩阵计算参数的区间估计,同时基于LR检验给出3种分布中相对最优分布的选择方法.从数值模拟的效果来看,EM算法的收敛性很强、精度较高;从新冠病毒肺炎现存确诊人数分布的拟合效果来看,0-1膨胀Beta-Negative Binomial分布更适合描述我国34个地区现存确诊人数的分布状况.

Entanglement properties between two atoms in the binomial optical field interacting with two entangled atoms

The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.

Wigner function for squeezed negative binomial state and evolution of density operator for amplitude decay

Using the thermal-entangled state representation and the operator-ordering method, we investigate Wigner function(WF) for the squeezed negative binomial state(SNBS) and the analytical evolution law of density operator in the amplitude decay channel.The results show that the analytical WF is related to the square of the module of single-variable Hermite polynomials, which leads to a new two-variable special function and its generating function, and the parameters s and γplay opposite roles in the WF distributions.Besides, after undergoing this channel, the initial pure SNBS evolves into a new mixed state related to two operator Hermite polynomials within normal ordering, and fully loses its nonclassicality and decays to vacuum at long decay time.

NUMERICAL ANALYSIS ON BINOMIAL TREE METHODS FOR AMERICAN LOOKBACK OPTIONS

Lookback options are path-dependent options. In general, the binomial tree methods, as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookback options. However, for floating strike lookback options, a single-state variable binomial tree method can be constructed. This paper is devoted to the convergence analysis of the single-state binomial tree methods both for discretely and continuously monitored American floating strike lookback options. We also investigate some properties of such options, including effects of expiration date, interest rate and dividend yield on options prices, properties of optimal exercise boundaries and so

Joint and supremum distributions in the compound binomial model with Markovian environment

In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.