On some compound distributions with Borel summands

The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a recursive structure for certain compound shifted Delaporte mixtures with Borel summands. Our models are introduced in an actuarial context as claim number distributions and are derived only with probabilistic arguments and elementary combinatorial identities. In the actuarial context related compound distributions are of importance as models for the total size of insurance claims for which we present simple recursion formulas of Panjer type.     

On a partial integrodifferential equation of Seal’s type

In this paper we generalize a partial integrodifferential equation satisfied by the finite time ruin probability in the classical Poisson risk model. The generalization also includes the bivariate distribution function of the time of and the deficit at ruin. We solve the partial integrodifferential equation by Laplace transforms with the help of Lagrange’s implicit function theorem. The assumption of mixed Erlang claim sizes is then shown to result in tractable computational formulas for the finite time ruin probability as well as the bivariate distribution function of the time of and the deficit at ruin. A more general partial integrodifferential equation is then briefly considered.     

Limit distribution of the coefficients of polynomials with only unit roots

We consider sequences of random variables whose probability generating functions have only roots on the unit circle, which has only been sporadically studied in the literature. We show that the random variables are asymptotically normally distributed if and only if the fourth central and normalized (by the standard deviation) moment tends to 3, in contrast to the common scenario for polynomials with only real roots for which a central limit theorem holds if and only if the variance is unbounded. We also derive a representation theorem for all possible limit laws and apply our results to many concrete examples in the literature, ranging from combinatorial structures to numerical analysis, and from probability to analysis of algorithms. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,707–738, 2015     

Estimation of rating classes and default probabilities in credit risk models with dependencies

Let Y = m(X) + ε be a regression model with a dichotomous output Y and a one‐step regression function m . In the literature, estimators for the three parameters of m , that is, the breakpoint θ and the levels a and b , are proposed for independent and identically distributed (i.i.d.) observations. We show that these standard estimators also work in a non‐i.i.d. framework, that is, that they are strongly consistent under mild conditions. For that purpose, we use a linear one‐factor model for the input X and a Bernoulli mixture model for the output Y . The estimators for the split point and the risk levels are applied to a problem arising in credit rating systems. In particular, we divide the range of individuals' creditworthiness into two groups. The first group has a higher probability of default and the second group has a lower one. We also stress connections between the standard estimator for the cutoff θ and concepts prevalent in credit risk modeling, for example, receiver operating characteristic. Copyright © 2014 John Wiley & Sons, Ltd.     

基于语义的软件服务故障自动诊断模型

模仿学习是机器人仿生机制研究的主要内容之一,即通过观察、理解、学习、模仿示教行为实现机器人的仿生特性。基于高斯过程分别表达采集离散示教信号所构成的示教轨迹和含有未知参数策略的模仿轨迹,构建模仿学习方法框架,将概率模型匹配引入到模仿学习中,以KL散度为代价函数比较两种轨迹的概率分布,运用梯度下降法寻求使KL散度最小的最优模仿控制策略,将策略应用于模仿机器人以完成与示教相同的模仿任务。以关节型机器人的机械臂摆动行为模仿为学习任务进行仿真,结果表明基于概率轨迹匹配的模仿学习方法能够实现机械臂摆动行为模仿,学习过程较传统方法简易且学习效果较好。     

铯47D精细能级超冷里德堡原子自由演化的动力学研究

用连续窄线宽激光器将超冷铯里德堡原子分别激发到47D_3/2, 47D_5/2精细态, 观察了处于里德堡精细态的铯原子向超冷铯等离子体自由演化的过程, 详细对比了不同精细态的铯里德堡原子预电离时间、电离速率以及等离子体的转化效率. 将里德堡原子快速转化为等离子体的过程解释为局域势阱内由预电离产生的电子与里德堡原子的快速碰撞导致的雪崩电离.     

基于HMM的机载设备状态健康评估方法研究

针对机载设备的状态健康评估问题,采用隐马尔科夫模型(HMM)对其进行性能退化程度的评估。首先引入状态条件概率矢量对HMM进行不确定性改进,并推导了其表达式;其次以状态条件概率比值为基础,给出了机载设备状态等级量化分值的计算方法,并据此设计了机载设备状态健康评估流程。最后以飞机发动机温控放大器为例进行仿真验证,结果表明上述方法能够给出直观、准确的状态评估结果。