Discrete Hazard Rate Research Articles

Compromises in occupational choice and premature termination of vocational education and training: gender type, prestige, and occupational interests in focus

This study examines whether premature termination of vocational education and training (VET) is more likely when trainees have to make compromises between their realistic occupational aspirations and the occupation for which they are trained in terms of the occupational dimensions of gender type, prestige, and occupational interests. Specifically, it examines the relative importance of the three compromise dimensions on premature VET termination. The study is based on a sample of 3,241 VET entrants from a cohort of ninth graders in 2010 in the German National Educational Panel Study (NEPS-SC4) in combination with aggregated data on occupational characteristics. Results from discrete hazard rate models indicate a higher risk of premature VET termination for trainees whose VET occupation differs from their realistic occupational aspiration from their school days. While compromises in prestige have no overall effect, both compromises in interests and gender type threaten the stability of VET. The results also indicate that compromises in interests have the strongest effect on the risk of premature VET termination and that the effects of compromises in gender type are partly mediated by the effects of compromises in interests. Furthermore, sensitivity analysis revealed that the main effects of compromises in gender type and prestige are gender specific.

Online Policies for Efficient Volunteer Crowdsourcing

Nonprofit crowdsourcing platforms such as food recovery organizations rely on volunteers to perform time-sensitive tasks. Thus, their success crucially depends on efficient volunteer utilization and engagement. To encourage volunteers to complete a task, platforms use nudging mechanisms to notify a subset of volunteers with the hope that at least one of them responds positively. However, because excessive notifications may reduce volunteer engagement, the platform faces a tradeoff between notifying more volunteers for the current task and saving them for future ones. Motivated by these applications, we introduce the online volunteer notification problem, a generalization of online stochastic bipartite matching where tasks arrive following a known time-varying distribution over task types. Upon arrival of a task, the platform notifies a subset of volunteers with the objective of minimizing the number of missed tasks. To capture each volunteer’s adverse reaction to excessive notifications, we assume that a notification triggers a random period of inactivity, during which she will ignore all notifications. However, if a volunteer is active and notified, she will perform the task with a given pair-specific match probability that captures her preference for the task. We develop an online randomized policy that achieves a constant-factor guarantee close to the upper bound we establish for the performance of any online policy. Our policy and hardness results are parameterized by the minimum discrete hazard rate of the interactivity time distribution. The design of our policy relies on sparsifying an ex ante feasible solution by solving a sequence of dynamic programs. Furthermore, in collaboration with Food Rescue U.S., a volunteer-based food recovery platform, we demonstrate the effectiveness of our policy by testing it on the platform’s data from various locations across the United States. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Acceptance reliability sampling plan for discrete lifetime models

Various types of acceptance reliability sampling plans have been reported in the literature. Most of the existing studies deal with the lifetimes of items described by continuous distributions. However, discrete lifetimes are also frequently encountered in practice. For example, field failures are often collected and reported daily, weekly, and so forth. Items often operate in cycles and the experimenter observes the number of cycles successfully completed prior to failure. In this study, we develop a variables acceptance reliability sampling plan for items having discrete lifetimes. Furthermore, the reliability improvement in the population reliability characteristics after the testing procedure, as compared to those before the test, is discussed in detail. The reliability sampling acceptance test is applied for heterogeneous populations using the alternative discrete hazard rate for the corresponding proportional hazards model. Some numerical examples illustrate our findings.

Continuous and discrete-time survival prediction with neural networks

Due to rapid developments in machine learning, and in particular neural networks, a number of new methods for time-to-event predictions have been developed in the last few years. As neural networks are parametric models, it is more straightforward to integrate parametric survival models in the neural network framework than the popular semi-parametric Cox model. In particular, discrete-time survival models, which are fully parametric, are interesting candidates to extend with neural networks. The likelihood for discrete-time survival data may be parameterized by the probability mass function (PMF) or by the discrete hazard rate, and both of these formulations have been used to develop neural network-based methods for time-to-event predictions. In this paper, we review and compare these approaches. More importantly, we show how the discrete-time methods may be adopted as approximations for continuous-time data. To this end, we introduce two discretization schemes, corresponding to equidistant times or equidistant marginal survival probabilities, and two ways of interpolating the discrete-time predictions, corresponding to piecewise constant density functions or piecewise constant hazard rates. Through simulations and study of real-world data, the methods based on the hazard rate parametrization are found to perform slightly better than the methods that use the PMF parametrization. Inspired by these investigations, we also propose a continuous-time method by assuming that the continuous-time hazard rate is piecewise constant. The method, named PC-Hazard, is found to be highly competitive with the aforementioned methods in addition to other methods for survival prediction found in the literature.

Online Policies for Efficient Volunteer Crowdsourcing

Nonprofit crowdsourcing platforms such as food recovery organizations rely on volunteers to perform time sensitive tasks. Thus, their success crucially depends on efficient volunteer utilization and engagement. To encourage volunteers to complete a task, platforms use nudging mechanisms to notify a subset of volunteers with the hope that at least one of them responds positively. However, since excessive notifications may reduce volunteer engagement, the platform faces a trade-off between notifying more volunteers for the current task and saving them for future ones. Motivated by these applications, we introduce the online volunteer notification problem, a generalization of online stochastic bipartite matching where tasks arrive following a known time-varying distribution over task types. Upon arrival of a task, the platform notifies a subset of volunteers with the objective of minimizing the number of missed tasks. To capture each volunteer’s adverse reaction to excessive notifications, we assume that a notification triggers a random period of inactivity, during which she will ignore all notifications. However, if a volunteer is active and notified, she will perform the task with a given pair-specific match probability that captures her preference for the task. We develop an online randomized policy that achieves a constant-factor guarantee close to the upper bound we establish for the performance of any online policy. Our policy as well as hardness results are parameterized by the minimum discrete hazard rate of the inter-activity time distribution. The design of our policy relies on sparsifying an ex-ante feasible solution by solving a sequence of dynamic programs. Further, in collaboration with Food Rescue U.S., a volunteer-based food recovery platform, we demonstrate the effectiveness of our policy by testing it on the platform's data from various locations across the U.S.

Multivariate discrete scalar hazard rate

In the present paper, we study the properties of the multivariate discrete scalar hazard rate. Its continuous analogue introduced in the early seventies did not attract much attention because it could not be used to identify the corresponding life distribution. We find the conditions under which an n-variate discrete scalar hazard rate can determine the distribution uniquely. Several other properties of this hazard rate which can be employed in modelling lifetime data are discussed. Some ageing classes based on the scalar hazard function are suggested.

Bimodal mortality dynamics for uveal melanoma: a cue for metastasis development traits?

BackgroundThe study estimates mortality dynamics (event-specific hazard rates over a follow-up time interval) for uveal melanoma.MethodsThree thousands six hundred seventy two patients undergoing radical or conservative treatment for unilateral uveal melanoma, whose yearly follow-up data were reported in three published datasets, were analysed. Mortality dynamics was studied by estimating with the life-table method the discrete hazard rate for death. Smoothed curves were obtained by a Kernel-like smoothing procedure and a piecewise exponential regression model. The ratio deaths/patients at risk per year was the main outcome measure.ResultsThe three explored hazard rate curves display a common bimodal pattern, with a sudden increase peaking at about three years, followed by reduction until the sixth-seventh year and a second surge peaking at about nine years after treatment.ConclusionsThe bimodal pattern of mortality indicates that uveal melanoma metastatic development cannot be explained by a continuous growth model. Similar metastasis dynamics have been reported for other tumours, including early breast cancer, for which it supported a paradigm shift to an interrupted growth model, the implications of which are episodes of ‘tumour dormancy’. We propose that the concepts of tumour homeostasis, tumour dormancy and enhancement of metastasis growth related to primary tumour removal, convincingly explaining the clinical behaviour of breast cancer, may be used for uveal melanoma as well. To confirm this proposition, a careful analysis of uveal melanoma metastasis dynamics is strongly warranted.

Models for predicting default: towards efficient forecasts

Purpose– The purpose of this paper is to assess and compare the forecast ability of existing credit risk models, answering three questions: Can these methods adequately predict default events? Are there dominant methods? Is it safer to rely on a mix of methodologies?Design/methodology/approach– The authors examine four existing models: O-score, Z-score, Campbell, and Merton distance to default model (MDDM). The authors compare their ability to forecast defaults using three techniques: intra-cohort analysis, power curves and discrete hazard rate models.Findings– The authors conclude that better predictions demand a mix of models containing accounting and market information. The authors found evidence of the O-score's outperformance relative to the other models. The MDDM alone in the sample is not a sufficient default predictor. But discrete hazard rate models suggest that combining both should enhance default prediction models.Research limitations/implications– The analysed methods alone cannot adequately predict defaults. The authors found no dominant methods. Instead, it would be advisable to rely on a mix of methodologies, which use complementary information.Practical implications– Better forecasts demand a mix of models containing both accounting and market information.Originality/value– The findings suggest that more precise default prediction models can be built by combining information from different sources in reduced-form models and combining default prediction models that can analyze said information.

What Went Wrong? Examining Moody’s Rated CDO Data

The downgrading of the tranches of Collateralized Debt Obligation (CDO) products backed by real estate related assets has caused severe disruptions in the housing and financial markets. The rating agencies have been criticized for the opacity in the rating process of the CDO products and also for giving the CDO tranches higher ratings than they deserved. However, not enough attention has been paid to the decision making process of the agencies to downgrade the CDO tranches. We use data from Moody’s CDO database to reconstruct the process through which Moody’s eventually downgraded the tranches. We use a discrete hazard rate model to study the variables that were relevant in the downgrading of the tranches of the CDOs. The empirical results show that out of the many CDO specific variables relevant to their ratings made available by Moody’s few have any explanatory power beyond the Moody’s Deal Scores (MDS). We show that the MDS could be explained by the changes in the Case-Shiller Composite-20 Index and Markit ABX.HE indices. Further analysis shows that Moody’s mostly relied on the changes in the Case-Shiller indexes in revising the MDS.

Semiparametric smoothing of discrete failure time data

An estimator of the hazard rate function from discrete failure time data is obtained by semiparametric smoothing of the (nonsmooth) maximum likelihood estimator, which is achieved by repeated multiplication of a Markov chain transition-type matrix. This matrix is constructed so as to have a given standard discrete parametric hazard rate model, termed the vehicle model, as its stationary hazard rate. As with the discrete density estimation case, the proposed estimator gives improved performance when the vehicle model is a good one and otherwise provides a nonparametric method comparable to the only purely nonparametric smoother discussed in the literature. The proposed semiparametric smoothing approach is then extended to hazard models with covariates and is illustrated by applications to simulated and real data sets.

Some Aspects of Discrete Hazard Rate Function in Telescopic Families

In this paper some reliability concepts in the telescopic family of distributions are compared. The telescopic family is named after the telescopic series in mathematics and represents an interesting class of discrete life time distributions. The telescopic family is introduced and also some conditions being equivalent to the IFR property are presented.

The dynamic nature of survival determinants in e-commerce

The dynamic effects of survival determinants in e-commerce are tested using longitudinal data on 460 e-tailers. This is achieved through the incorporation of both time-varying covariates and coefficients in a discrete hazard rate model. The model includes elements of competitive strategy, industry structure, firm and product characteristics, and the macro environment. The study demonstrates the changing effect over time of factors affecting survival. For example, order of entry advantages are observed, but they are short-lived. This finding shows that e-tailers cannot rely on early entry as a strategic move in the long run. E-tailers with more media presence seem to survive longer. Being publicly traded and selling products with digital characteristics present advantages for e-tailers only in the beginning years, but they are not sustainable over long time periods. Survival chances decrease with higher competitive density, market growth rate, and equity market level at the time of entry. Conversely, economic growth tends to increase survival chances. The study also finds an inverted-U relationship between the hazard of exit and firm age. The conclusion section discusses the implications of the time-varying nature of survival determinants.

Leaving Unemployment for Self-employment A Discrete Duration Analysis of Determinants and Stability of Self-employment among Former Unemployed

The paper investigates the determinants and the success of self-employment among former unemployed. Self-employment has become an important re-employment opportunity during the last decade due to increasing subsidies. The econometric analysis is carried out using discrete hazard rate models on 14 waves of the German Socio-Economic Panel, covering the period from 1983 to 1996. I do not find any effects of unemployment duration on the transition from unemployment to selfemployment. Moreover, unemployed people entering self-employment have higher skills than the average of the unemployed population and self-employment seems to be more stable than paid-employment would have been because people face a lower risk of becoming unemployed again.

Employment Effects of Publicly Financed Training Programs – The East German Experience / Beschäftigungseffekte von Fortbildungs- und Umschulungsmaßnahmen in Ostdeutschland

Summary We analyze the effectiveness of publicly financed training and retraining programs in east Germany as measured by their effects on individual re-employment probabilities after training. These are estimated by discrete hazard rate models on the basis of individual-level panel data. We account for unobserved individual heterogeneity in both the training participation and outcome equation. The latter differentiates between transitions into “stable” and “unstable” employment after the completion of a training program. Our findings are that in the first phase of the east German transition process, when the institutions delivering the training programs were being set up, there are no positive effects of training on the probability to find stable employment. For the period of September 1992 to November 1994, when the institutional structure for the programs was in place, we find positive effects of both on-the-job and off-the-job training for women, and positive effects of off-the-job training for men.

Mixture models in hazard rates estimation

We propose to use mixture of geometries to model the duration Ot a spell in discrete time. The discrete hazard rate can be determined by the moments of the mixing distribution through the qd(quotient difference) algorithm, By introducing a sequence of parameters called canonical moments, we can ensure the resulting estimate of the mixing distribution is supported on [0,1]. Using the bootstrap method, we can construct, instantaneous confidence intervals for the hazard rates. For the continuous time, a mixture of exponentials is proposed. By a simple transformation, the problem can be reduced to the case for mixture of geometries. The instantaneous confidence intervals for the hazard rates can be constructed.

Discrete hazard rate functions

Discrete hazard rate functions are a useful tool for modeling joint distributions of discrete lifetimes. In this paper we study a dynamic approach to discrete reliability theory based on discrete hazard rate functions. The hazard rate functions are first defined and studied in the univariate case. Then the general multivariate case is considered. Necessary and sufficient conditions are given for a set of functions to be discrete multivariate conditional hazard rate functions. An application of the hazard rate functions, to characterizations of aging properties of discrete lifetimes distributions, is described. Further applications of these functions to modelings of univariate and multivariate discrete imperfect repair are also included. Some examples illustrate the theory.

The score statistic in constancy testing for a discrete hazard rate : D. A. Schiffman. IEEE Trans. Reliab.R-35 (5), 590 (1986)

The score statistic in constancy testing for a discrete hazard rate : D. A. Schiffman. IEEE Trans. Reliab.R-35 (5), 590 (1986)

The Score Statistic in Constancy Testing for a Discrete Hazard Rate

In discrete failure analysis, variable hazard-rate functions can often yield the constant hazard rate as a special case. In many such instances it is of interest to test statistically, using failure data, whether the hazard rate is constant or variable. The purpose of this article is to examine, using examples, the advantages of the score statistic in such tests. While the score statistic is based on the gradient of the log-likelihood function, the complexities often associated with maximum likelihood estimation and testing do not arise when the score statistic is used to test the constancy of the hazard rate. In particular, the appropriate score statistic can be calculated using simple linear least-squares regression techniques. The results are applied to failure data on electrical power transformers.