Analysis of a continuous-time proportional hazard model using discrete duration data

Many economic duration variables are often available only up to intervals, and not up to exact points. However, continuous time duration models are conceptually superior to discrete ones. Hence, in duration analyses, one faces a situation with discrete data and a continuous model. This paper discusses (i) the asymptotic bias of a conventional approximation procedure in which a discrete duration is treated as an exact observation; and (ii) the efficiency of a correct maximum likelihood estimator which appropriately accounts for the discrete nature of the data.     

Applicability of a Neuroprobabilistic Integral Risk Index for the Environmental Management of Polluted Areas: A Case Study

Recently, we developed a GIS-Integrated Integral Risk Index (IRI) to assess human health risks in areas with presence of environmental pollutants. Contaminants were previously ranked by applying a self-organizing map (SOM) to their characteristics of persistence, bioaccumulation, and toxicity in order to obtain the Hazard Index (HI). In the present study, the original IRI was substantially improved by allowing the entrance of probabilistic data. A neuroprobabilistic HI was developed by combining SOM and Monte Carlo analysis. In general terms, the deterministic and probabilistic HIs followed a similar pattern: polychlorinated biphenyls (PCBs) and light polycyclic aromatic hydrocarbons (PAHs) were the pollutants showing the highest and lowest values of HI, respectively. However, the bioaccumulation value of heavy metals notably increased after considering a probability density function to explain the bioaccumulation factor. To check its applicability, a case study was investigated. The probabilistic integral risk was calculated in the chemical/petrochemical industrial area of Tarragona (Catalonia, Spain), where an environmental program has been carried out since 2002. The risk change between 2002 and 2005 was evaluated on the basis of probabilistic data of the levels of various pollutants in soils. The results indicated that the risk of the chemicals under study did not follow a homogeneous tendency. However, the current levels of pollution do not mean a relevant source of health risks for the local population. Moreover, the neuroprobabilistic HI seems to be an adequate tool to be taken into account in risk assessment processes.     

农产品电商集群企业地理邻近性对协同创新绩效的影响

基于知识治理视角,构建农产品电商集群企业地理邻近性、知识治理、知识共享和协同创新绩效关系的链式中介模型,并引入网络关系强度作为调节变量,结合341家农产品电商集群企业的调研数据,采用多层次回归和Bootstrap分析方法,分析地理邻近性对协同创新绩效的直接作用,检验知识治理和知识共享的独立中介作用和链式中介作用,以及网络关系强度的调节作用。结果表明：地理邻近性正向影响协同创新绩效;知识治理在地理邻近性和协同创新绩效间发挥中介作用;知识共享在知识治理和协同创新绩效间发挥中介作用;知识治理和知识共享在地理邻近性和协同创新绩效间发挥链式中介作用;网络关系强度正向调节正式知识治理和显性知识共享的链式中介作用。因此,农产品电商集群企业要把握数字经济发展契机,善于利用集群区位优势和产业资源,激发正式知识治理和非正式知识治理的双重效应,与合作企业建立良好的知识共享关系,实现高质量协同创新发展。     

Hazard rate ordering of the second-order statistics from multiple-outlier PHR samples

In this paper, we compare the hazard rate functions of the second-order statistics arising from two sets of independent multiple-outlier proportional hazard rates (PHR) samples. It is proved that the submajorization order between the sample size vectors together with the supermajorization order between the hazard rate vectors imply the hazard rate ordering between the corresponding second-order statistics from multiple-outlier PHR random variables. The results established here provide theoretical guidance both for the winner's price for the bid in the second-price reverse auction in auction theory and fail-safe system design in reliability. Some numerical examples are also provided for illustration.     

Elasticity function of a discrete random variable and its properties

Elasticity (or elasticity function) is a new concept that allows us to characterize the probability distribution of any random variable in the same way as characteristic functions and hazard and reverse hazard functions do. Initially defined for continuous variables, it was necessary to extend the definition of elasticity and study its properties in the case of discrete variables. A first attempt to define discrete elasticity is seen in Veres-Ferrer and Pavía (2014a). This paper develops this definition and makes a comparative study of its properties, relating them to the properties shown by discrete hazard and reverse hazard, as both defined in Chechile (2011). Similar to continuous elasticity, one of the most interesting properties of discrete elasticity focuses on the rate of change that this undergoes throughout its support. This paper centers on the study of the rate of change and develops a set of properties that allows us to carry out a detailed analysis. Finally, it addresses the calculation of the elasticity for the resulting variable obtained from discretizing a continuous random variable, distinguishing whether its domain is in real positives or negatives.     

Classical estimation of hazard rate and mean residual life functions of Pareto distribution

Abstract

In this paper we find the maximum likelihood estimates (MLEs) of hazard rate and mean residual life functions (MRLF) of Pareto distribution, their asymptotic non degenerate distribution, exact distribution and moments. We also discuss the uniformly minimum variance unbiased estimate (UMVUE) of hazard rate function and MRLF. Finally, two numerical examples with simulated data and real data set, are presented to illustrate the proposed estimates.     

A New Quantile Function with Applications to Reliability Analysis

In this article, we propose a new class of distributions defined by a quantile function, which nests several distributions as its members. The quantile function proposed here is the sum of the quantile functions of the generalized Pareto and Weibull distributions. Various distributional properties and reliability characteristics of the class are discussed. The estimation of the parameters of the model using L-moments is studied. Finally, we apply the model to a real life dataset.     

Use of log−log survival function in modeling time-covariate interactions in Cox regression

Plotting of log−log survival functions against time for different categories or combinations of categories of covariates is perhaps the easiest and most commonly used graphical tool for checking proportional hazards (PH) assumption. One problem in the utilization of the technique is that the covariates need to be categorical or made categorical through appropriate grouping of the continuous covariates. Subjectivity in the decision making on the basis of eye-judgment of the plots and frequent inconclusiveness arising in situations where the number of categories and/or covariates gets larger are among other limitations of this technique. This paper proposes a non-graphical (numerical) test of the PH assumption that makes use of log−log survival function. The test enables checking proportionality for categorical as well as continuous covariates and overcomes the other limitations of the graphical method. Observed power and size of the test are compared to some other tests of its kind through simulation experiments. Simulations demonstrate that the proposed test is more powerful than some of the most sensitive tests in the literature in a wide range of survival situations. An example of the test is given using the widely used gastric cancer data.     

Estimating the effectiveness of a misdemeanor drug diversion program using propensity score matching and survival analyses

This study analyzes three years of data on misdemeanor drug offenders in Winnebago County, Wisconsin. A portion of these offenders opted into a Misdemeanor Drug Diversion Program (MDDP) offered instead of traditional adjudication. Recidivism in the treatment and comparison groups is estimated using standard binary response techniques augmented with propensity score matching to address selection bias. Results show that the MDDP reduces the probability of re-offense by 16%, after adjusting for possible selection bias. Cox proportional hazard modeling is also used to assess time-to-re-offense differentials between the treatment and comparison groups. The survival analysis indicates that the hazard rate of re-offense is 60% lower per day among those treated with the MDDP program than those who did not complete the program. The average number of days to re-offense among those that do re-offend is 297 days in the treatment group and 203 days in the comparison group.     

Order statistics from the linear-exponential distribution,part I: increasing hazard rate case

For the linear-exponential distribution with increasing hazard rate, exact and explicit expressions for means, product moments and percentage points of order statistics are obtained. Some recurrence relations for both single and product moments of order statistics are also derived. These recurrence relations would enable one to obtain all the higher order moments of order statistics for all sample sizes from those of the lower order