随着社会的不断发展和死亡率的下降,死亡率数据分析及未来预测一直是精算师、人口学家和统计学家的研究重点。经典的单因子Lee-Carter模型通过对数转换将死亡率分解为年龄和时间项,尽管形式简单,但在处理复杂死亡率模式时表现有限。为此,我们采用了神经网络DNN模型,通过多层神经网络捕捉数据中的非线性关系,期望有所改善。同时,在经典Heligman-Pollard模型的基础上,引入了动态分量和随机游走结构,放宽了参数平稳性假设,从而能更精准地描述不同年龄段死亡率的变化。我们还使用GMRF模型,通过高效捕捉跨年龄组和跨年份的死亡率相关性,并通过基于梯度的MCMC采样器提高采样效率,以期减少误差。最后,结合均方根误差(RMSE)、平均绝对误差(MAE)和平均绝对百分比误差(MAPE)等评价指标,对不同模型的结果进行了比较分析。结果表明,GMRF模型在预测精度方面表现最佳,Heligman-Pollard模型适用于描述死亡率的动态变化,而DNN模型则适合于大规模数据且需捕捉非线性关系的场景。With society’s development and declining mortality rates, mortality data analysis and forecasting have been key research areas for actuaries, demographers, and statisticians. The Lee-Carter model decomposes mortality into age and time components using a logarithmic transformation. While simple, it has limitations in handling complex mortality patterns. To improve, we used a neural network (DNN) model to capture nonlinear relationships in the data. Additionally, we enhanced the Heligman-Pollard model with dynamic components and random walk structure, allowing more accurate description of age-specific mortality changes. We also use GMRF model to capture the mortality correlation across age groups and years efficiently, and improve the sampling efficiency through gradient-based MCMC sampler in order to reduce errors. Finally, we compared the model’s using metrics like RMSE, MAE, and MAPE. The results show that the GMRF model performs best in accuracy, the Heligman-Pollard model excels at describing dynamic mortality changes, and the DNN model is best for large datasets with nonlinear relationships.
该文讨论在伪欧氏空间中,带有以下初始条件的拉格朗日平均曲率流方程{ dY(x,t)dt=HY(x,0)=Y0(x)。其中,该方程等价于特殊拉格朗日抛物方程{ ∂u∂t=Fτ(D2u), t>0,x∈ℝnu=u0(x), t=0,x∈ℝn。通过构造函数,将证明若0τπ4或π4τπ2,该抛物方程存在唯一光滑解u(x,t),且存在更高阶导数的衰减估计。另一方面,应用Arzelà-Ascoli定理来获得u(x,t)收敛到拉格朗日平均曲率流方程的自膨胀解。In this paper, we consider the Lagrangian mean curvature flow equation in pseudo-Euclidean space with the initial value: { dY(x,t)dt=HY(x,0)=Y0(x). This equation is equivalent to the special Lagrangian parabolic equation { ∂u∂t=Fτ(D2u), t>0,x∈ℝnu=u0(x), t=0,x∈ℝn. By constructing a suitable function, it is proven that if 0τπ4or π4τπ2, the parabolic equation has a unique smooth solution u(x,t)and decay estimates for higher-order derivatives exist. On the other hand, the Arzelà-Ascoli theorem is applied to obtain the convergence of u(x,t)to the self-expanding solution of the Lagrangian mean curvature flow equation.
在大数据时代,总体往往呈现出显著的异质性特点。本文借助混合模型来刻画了多个同质个体构成总体的异质性。我们基于改进比例反失效率模型的参数来体现种群中的信息,探讨了改进比例反失效率模型构成有限混合模型的统计性质,结合矩阵链优序或向量的优化序和T转换矩阵,研究了有限混合模型参数和混合比例的随机性质,给出了两组异质有限混合总体普通随机序成立的充分条件,丰富了异质有限混合总体的随机比较理论。With the advent of the big data era, populations frequently display distinct heterogeneity characteristics. This paper uses mixture models to characterize the heterogeneity of populations composed of multiple homogeneous individuals. Based on the parameters of a modified proportional reversed hazard rate model, we incorporate information from the population and explore the statistical properties of a finite mixture model formed by the modified proportional reversed hazard rate model. By combining matrix chain optimization or the optimization sequence of vectors with the T-transformation matrix, we study the stochastic properties of the finite mixture model’s parameters and mixing proportions. Sufficient conditions for the establishment of ordinary stochastic order for two heterogeneous finite mixture populations are provided, enriching the theory of stochastic comparisons for heterogeneous finite mixture populations.
本文研究同类平行机环境下的在线排序问题,其中工件具有任意到达时间,目标为最小化最大完工时间.所讨论机器的速度,除了最后一台为s(s>1)外,其余m−1台机器的速度均为1.本文分析了列表(list scheduling,LS)算法的性能,得到了机器数m=2及m≥3时LS算法的竞争比分别为2/3+√5和4−4/m+1,并在一般情形下设计了一个竞争比不超过3.8626的更好的算法—改良列表(modified list scheduling,MLS)算法.
本文主要研究了FGM Copula相依下随机变量二阶顺序统计量的随机比较,给出了二阶顺序统计量之间普通随机序、增凸序与增凹序关系成立的充分条件,并通过数值例子说明了主要结论。This paper investigates the stochastic comparison of se...
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本文主要研究了FGM Copula相依下随机变量二阶顺序统计量的随机比较,给出了二阶顺序统计量之间普通随机序、增凸序与增凹序关系成立的充分条件,并通过数值例子说明了主要结论。This paper investigates the stochastic comparison of second-order statistics from dependent random samples with FGM Copula. Sufficient conditions are established on the usual stochastic order, the increasing convex order and the increasing concave order for the second-order statistic. And some numerical examples are provided to illustrate the theoretical results.
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