Modeling Lifetimes by a Stochastic Process Hitting a Critical Point

First hitting times arise naturally in survival analysis where the underlying stochastic counting process represents the strength of the health of an individual. The patient experiences a clinical endpoint when this process reaches a critical point for the first time. We propose a very flexible and unified first hitting time density function in a stochastic carcinogenesis counting process, and its mathematical properties are investigated. The Poisson and negative binomial first hitting time models are addressed and two examples with real data are presented.     

On Some Optimal Bayesian Nonparametric Rules for Estimating Distribution Functions

In this paper, we present a novel approach to estimating distribution functions, which combines ideas from Bayesian nonparametric inference, decision theory and robustness. Given a sample from a Dirichlet process on the space (𝒳, A), with parameter η in a class of measures, the sampling distribution function is estimated according to some optimality criteria (mainly minimax and regret), when a quadratic loss function is assumed. Estimates are then compared in two examples: one with simulated data and one with gas escapes data in a city network.     

A new generation of process capability indices based on fuzzy measurements

Process capability indices (PCIs) provide numerical measures on whether a process conforms to the defined manufacturing capability prerequisite. These have been successfully applied by companies to compete with and to lead high-profit markets by evaluating the quality and productivity performance. The PCI C_p compares the output of a process to the specification limits (SLs) by forming the ratio of the width between the process SLs with the width of the natural tolerance limits which is measured by six process standard deviation units. As another common PCI, C_pm incorporates two variation components which are variation to the process mean and deviation of the process mean from the target. A meaningful generalized version of above PCIs is introduced in this paper which is able to handle in a fuzzy environment. These generalized PCIs are able to measure the capability of a fuzzy-valued process in producing products on the basis of a fuzzy quality. Fast computing formulas for the generalized PCIs are computed for normal and symmetric triangular fuzzy observations, where the fuzzy quality is defined by linear and exponential fuzzy SLs. A practical example is presented to show the performance of proposed indices.     

On the generalized process capability under simple and mixture models

Process capability (PC) indices measure the ability of a process of interest to meet the desired specifications under certain restrictions. There are a variety of capability indices available in literature for different interest variables such as weights, lengths, thickness, and the life time of items among many others. The goal of this article is to study the generalized capability indices from the Bayesian view point under different symmetric and asymmetric loss functions for the simple and mixture of generalized lifetime models. For our study purposes, we have covered a simple and two component mixture of Maxwell distribution as a special case of the generalized class of models. A comparative discussion of the PC with the mixture models under Laplace and inverse Rayleigh are also included. Bayesian point estimation of maintenance performance of the system is also part of the study (considering the Maxwell failure lifetime model and the repair time model). A real-life example is also included to illustrate the procedural details of the proposed method.     

Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure

The Dirichlet process is a fundamental tool in studying Bayesian nonparametric inference. The Dirichlet process has several sum representations, where each one of these representations highlights some aspects of this important process. In this paper, we use the sum representations of the Dirichlet process to derive explicit expressions that are used to calculate Kolmogorov, Lévy, and Cramér–von Mises distances between the Dirichlet process and its base measure. The derived expressions of the distance are used to select a proper value for the concentration parameter of the Dirichlet process. These tools are also used in a goodness-of-fit test. Illustrative examples and simulation results are included.     

Uniform Tail Asymptotics for the Sum of Two Correlated Classes with Stochastic Returns and Dependent Heavy Tails

Consider a continuous-time risk model with two correlated classes of insurance business and risky investments whose price processes are geometric Lévy processes. By assuming that the correlation comes from a common shock, and the claim sizes are heavy-tailed and pairwise quasi-asymptotically independent, we investigate the tail behavior of the sum of the stochastic present values of the two correlated classes, and a uniform asymptotic formula is obtained.     

基于工作过程的课程开发研究

基于工作过程的课程开发是当前我国职业教育进行课程改革的方向,本文结合作者长期教学改革与教学实践经验,根据国内现有的教学条件,以调查与统计分析课程为例,介绍了基于工作过程的课程开发与实践教学的尝试,具有较强的可操作性,对其他课程的开发具有一定的参考价值。     

以数学建模竞赛活动为平台培养大学生的科研能力

提出了如何利用数学建模竞赛活动培养大学生四个方面的科研能力,即搜索和整理资料的能力、运用计算机解决问题的能力、创新能力和论文撰写能力。通过对学生这四个方面的科研能力的培养,提高学生的科学素质。     

Deliberate Trust and Intuitive Faith: A Dual‐Process Model of Reliance

Drawing on the dual process framework from social and cognitive psychology, this paper reconciles two distinct conceptualizations of trust prevalent in the literature: “rational” calculative and irrational “affective” or normative. After critically reviewing previous attempts at reconciliation between these distinctions, we argue that the notion of trust as “reliance” is the higher order category of which “deliberate trust” and “intuitive faith” are subtypes. Our revised approach problematizes the conflation of epistemic uncertainty with phenomenological uncertainty while providing sound footing for a key sociological insight: that reliance on the routine social order is both the cognitive default and based on substantial practical evidence. We develop two broad suggestions for future research from these implications: (1) sociological research should examine the role of intuitive faith—as opposed to deliberate trust—in late modern societies, and (2) analysts should challenge the role of deliberate trust as the “modal” form of reliance in contemporary research.