Bivariate extension of (dynamic) cumulative past entropy

Recently, the concept of cumulative residual entropy (CRE) has been studied by many researchers in higher dimensions. In this article, we extend the definition of (dynamic) cumulative past entropy (DCPE), a dual measure of (dynamic) CRE, to bivariate setup and obtain some of its properties including bounds. We also look into the problem of extending DCPE for conditionally specified models. Several properties, including monotonicity, and bounds of DCPE are obtained for conditional distributions. It is shown that the proposed measure uniquely determines the distribution function. Moreover, we also propose a stochastic order based on this measure.     

On extreme order statistics from heterogeneous beta distributions with applications

This paper treats the problem of stochastic comparisons for the extreme order statistics arising from heterogeneous beta distributions. Some sufficient conditions involved in majorization-type partial orders are provided for comparing the extreme order statistics in the sense of various magnitude orderings including the likelihood ratio order, the reversed hazard rate order, the usual stochastic order, and the usual multivariate stochastic order. The results established here strengthen and extend those including Kochar and Xu (2007 Kochar, S.C., Xu, M. (2007). Stochastic comparisons of parallel systems when components have proportional hazard rates. Probab. Eng. Inf. Sci. 21:597–609.[Crossref], [Web of Science ®] , [Google Scholar]), Mao and Hu (2010 Mao, T., Hu, T. (2010). Equivalent characterizations on orderings of order statistics and sample ranges. Probab. Eng. Inf. Sci. 24:245–262.[Crossref], [Web of Science ®] , [Google Scholar]), Balakrishnan et al. (2014 Balakrishnan, N., Barmalzan, G., Haidari, A. (2014). On usual multivariate stochastic ordering of order statistics from heterogeneous beta variables. J. Multivariate Anal. 127:147–150.[Crossref], [Web of Science ®] , [Google Scholar]), and Torrado (2015 Torrado, N. (2015). On magnitude orderings between smallest order statistics from heterogeneous beta distributions. J. Math. Anal. Appl. 426:824–838.[Crossref], [Web of Science ®] , [Google Scholar]). A real application in system assembly and some numerical examples are also presented to illustrate the theoretical results.     

Examples of doubly stochastic measures supported on the graphs of two functions

A doubly stochastic measure (DSM) is a measure μ on the unit square so that μ([0, 1] × A) = μ(A × [0, 1]) = m(A) where m is Lebesgue measure. The set of DSMs forms a convex set in the space of measures. It is known that DSMs supported on the union of two graphs of invertible functions are extreme points of that convex set (Seethoff and Shiflett, 1977/78 Seethoff, T.L., Shiflett. (1977/78). Doubly stochastic measures with prescribed support. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 41(4):283–288.[Crossref], [Web of Science ®] , [Google Scholar]). In general, there are few examples of extreme points in the literature. There are examples of so-called hairpins where the functions involved are inverses of each other, but there are also examples of the union of the graphs of a function and its inverse does not support a DSM (Sherwood and Taylor, 1988 Sherwood, H., Taylor, M.D. (1988). Doubly stochastic measures with hairpin support. Probab. Theory Related Fields 78(4):617–626.[Crossref], [Web of Science ®] , [Google Scholar]). In this paper, for a function f in a certain class, we find companion functions g so that the union of the graphs of f and g support a DSM even though the union of the graphs of f and f-inverse do not.     

Role of stylized features in constructing better estimators

This article discusses the role played by stylized features of financial time series in constructing better estimators for the model parameters. We study in detail one such estimator for the transition probabilities of a simple regime switching model. The estimator is based on the squared autocovariances of the time series, which has been discussed in several empirical studies of economic and financial time series. The effectiveness of this estimator in improving the estimation accuracy is investigated, using both finite sample and asymptotic computations. We also report simulation results to confirm our findings and to extend our conclusions over a bigger region of the parameter space.     

Testing monotonic equilibrium residual entropy of N-State Random Evolution

In this study, we propose an information measure of uncertainty associated with the random equilibrium residual lifetime of a system driven by N-State Random Evolution. A U-statistic test driven by a moment inequality is proposed for testing the hypothesis that the uncertainty of equilibrium remaining life of a system remains unchanged (when system is in the steady state) against the alternative situation when system’s equilibrium residual life has increasing uncertainty over time (i.e., the life distribution has Increasing Equilibrium Residual Entropy property). Some numerical results such as tabulated critical values and empirical power of the proposed test statistic are presented as well.     

中国蔬菜价格波动与通货膨胀——基于波动来源的分解

利用Census X12季节调整和H-P滤波法,将蔬菜价格波动来源分解为趋势变动、季节变动、循环变动和不规则变动要素。利用Bootstrap因果检验与VAR模型,考察了蔬菜价格波动来源的分解因素与中国通货膨胀的关联性。结果表明,蔬菜价格波动影响消费者物价指数的主要渠道是通过季节变动和不规则变动要素;季节变动因素对消费者物价指数的影响呈季节周期性;不规则变动对消费者物价指数的冲击在最初时最显著,随后逐渐减弱。政策含义为,降低公众的通胀预期、促进蔬菜跨区域流通、控制蔬菜运输的物流成本、健全政府灾害天气应急响应机制均有利于减缓CPI上涨。     

基于广义误差分布的股票收益率波动特征分析

假设股票收益率序列服从具有厚尾特征的GED分布,利用多种非对称性模型描述和检验了沪市股票日收益率序列的波动性特征,发现股票价格波动具有条件异方差性,并通过对股票市场信息影响曲线的分析,刻画了沪市股票价格波动中的显著非对称性。这说明股市波动对于不同的政策干预和信息冲击具有不同程度的反应,且非对称性的方向与以往结论有所不同,说明我国股市风险变异特征和收益状况在不断的发生变化,＂利好消息＂对股市的刺激作用需要其他市场干预的配合才能发挥出来。     

多维汇率联动期权跳——扩散模型及其定价

在资产价格服从跳——扩散模型,汇率服从不同跳跃幅度的不连续模型的基础上,考虑用无套利分析方法得到了期权应满足的随机微分方程,并由Feynman-Kac公式,得到了多种欧式汇率联动期权的计算公式;当汇率联动期权具有随机寿命时,进一步研究了多种欧式汇率联动期权的价格。     

随机分形思想对农村经济合作组织建设的启示

农村经济增长乏力 ,已成为我国经济发展最重要的问题之一。本文通过对农村经济合作组织建设必要性的分析 ,指出了农村经济合作组织建设在农村经济发展及农村居民收入水平提高中的重要作用 ;并结合随机分形思想 ,提出了发展农村经济合作组织的若干思路 ;最后 ,指出了促进农村经济合作组织建设过程中应注意的几个问题。