Some general results for moments in bivariate distributions

The purpose of this paper is to present a closed formula to compute the moments of a general function from the knowledge of its bivariate survival function. The result is derived by utilizing an integration by parts formula for two variables, which is not readily available in the literature. Many of the existing results are obtained as special cases. Finally, two examples are presented to illustrate the results. In both the examples, mixed moments as well as moments for the series system and parallel system are obtained. The integration by parts formula in two variables, derived here, is of interest in its own right and we hope that it will be useful in other investigations. The integration by parts formula in two variables is derived as a special case of a general formula in n variables.     

New development: Regression-to-the-mean explains the otherwise puzzling coefficients in NHS England’s formula for funding CCGs

This paper reviews NHS England’s recent report on the formula that guides the allocation of tens of billions of pounds to clinical commissioning groups (CCGs). It finds deficiencies and errors in the unprincipled construction of the formula and substitutes Sir Francis Galton’s logical concept of ‘regression to the mean’ for the report’s ad hoc conjectures about striking patterns of certain coefficients.     

Target volatility option pricing in the lognormal fractional SABR model

We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula of Itô's calculus yields an approximation formula for the price of a target volatility option in small time by the technique of freezing the coefficient. A decomposition formula in terms of Malliavin derivatives is also provided. Alternatively, we also derive closed form expressions for a small volatility of volatility expansion of the price of a target volatility option. Numerical experiments show the accuracy of the approximations over a reasonably wide range of parameters.     

外推型预期公式的检验与评价

经济学中的很多变量需要预测,其中的一个方法是运用外推型预期公式。由于外推型预期公式有 其自身特点和规律,即趋势值的选择是影响预测效果的一个主要变量,因此使用该公式进行经济预测时, 短期预测应选择较小的趋势值,长期预测应选取中间的趋势值。     

关于曲线积分和曲面积分教学中几个难点的突破

加强曲线、曲面积分概念讲解,标准化曲线、曲面积分的计算程序,沟通有关积分之间关系,以消除学生 对斯托克斯等公式的深奥感,有效地突破了曲线、曲面积分教学中的几个难点。     

用基变换方法求多项式的泰勒公式

通过分析多项式函数f(x)在不同点处的泰勒公式与线性空间基变换的联系,得到了多项式在同点处泰勒公式的一种求解方法。     

Bridging the gap between a stationary point process and its Palm distribution

In the context of stationary point processes measurements are usually made from a time point chosen at random or from an occurrence chosen at random. That is, either the stationary distribution P or its Palm distribution P° is the ruling probability measure. In this paper an approach is presented to bridge the gap between these distributions. We consider probability measures which give exactly the same events zero probability as P°, having simple relations with P . Relations between P and P° are derived with these intermediate measures as bridges. With the resulting Radon-Nikodym densities several well-known results can be proved easily. New results are derived. As a corollary of cross ergodic theorems a conditional version of the well-known inversion formula is proved. Several approximations of P° are considered, for instance the local characterization of P^o as a limit of conditional probability measures P° N The total variation distance between P° and P₁ can be expressed in terms of the P-distribution function of the forward recurrence time.     

Covariance formulas via marginal martingw

Prenctice and Cai recently introduced and studied the function C defined as the covariance function of the two marginal counting process martingales of a pair of dependent survival times (T₁, T₂ ). They show that the function C together with the marginal distributions determines the joint survival function F of (T₁, T₂ ). In this note we show how the key characterizing equation of Prentice and Cai yields a formula for the covariance of T₁ and T₂ in termsof the marginal mean residual life functions and C. The resulting formula generalizes a formula for the variance of a one-dimensional random variable Tdueto Pyke (1965). We also explore several generalizations of the covariance formula, and obtain a valid k-dimensional version of the Prentice and Cai formula.     

长历时暴雨强度公式的推求方法

近年来,随着极端暴雨事件的出现,导致城市内涝灾害频繁发生,原有降雨历时仅为2h的市政排水设计暴雨强度公式已无法满足城市暴雨设计的需求,因此就要延长暴雨采样历时,推求出长历时(24h)暴雨强度公式。针对以上问题,根据北京市提供的52a(1961-2012)原始降雨资料并进行数字化处理,结合水利的长历时特点,采用兼顾市政排水,水利排涝,内涝防治的采样方法,应用P-Ⅲ分布曲线进行频率分析后采用6种经典方法推求暴雨强度公式的参数值,优选出误差最小且满足规范要求的暴雨强度公式参数值,进而推求长历时暴雨强度公式,在此基础上与短历时暴雨强度公式比较,分析两者的差异,为城市雨水排除规划设计提供科学依据和参考。     

任意空间位置两多边形多匝线圈的互感计算

根据聂以曼公式推导出任意空间位置两多边形线圈互感的一般表达式,应用旋转矩阵实现了线圈位置的变化,通过MATLAB软件编程计算,绘出了互感的变化曲线,并对计算结果进行进行了分析验证。