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In this article, we study the merging and splitting of generalized counting processes (GCPs). First, we study the merging of a finite number of independent GCPs and then extend it to the case of countably infinite. The merged process is observed to be a GCP with increased arrival rates. It is shown that a packet of jumps arrives in the merged process according to the Poisson process. Also, we study two different types of splitting of a GCP. In the first type, we study the splitting of jumps of a GCP where the probability of simultaneous jumps in the split components is negligible. In the second type, we consider the splitting of jumps in which there is a possibility of simultaneous jumps in the split components. It is shown that the split components are GCPs with certain decreased jump rates. Moreover, the independence of split components is established. Later, we discuss applications of the obtained results to industrial fishing problem and hotel booking management system. [ABSTRACT FROM AUTHOR]

The Riemann surface associated with counting the current between two states of an underlying Markov process is hyperelliptic. We explore the consequences of this property for the time-dependent probability of that current for Markov processes with generic transition rates. When the system is prepared in its stationary state, the relevant meromorphic differential is in particular fully characterized by the precise identification of all its poles and zeroes. [ABSTRACT FROM AUTHOR]

In statistical network analysis it is common to observe so called interaction data. Such data is characterized by actors forming the vertices and interacting along edges of the network, where edges are randomly formed and dissolved over the observation horizon. In addition, covariates are observed and the goal is to model the impact of the covariates on the interactions. We distinguish two types of covariates: global, system-wide covariates (i.e., covariates taking the same value for all individuals, such as seasonality) and local, dyadic covariates modeling interactions between two individuals in the network. Existing continuous time network models are extended to allow for comparing a completely parametric model and a model that is parametric only in the local covariates but has a global nonparametric time component. This allows, for instance, to test whether global time dynamics can be explained by simple global covariates like weather, seasonality etc. The procedure is applied to a bike-sharing network by using weather and weekdays as global covariates and distances between the bike stations as local covariates. [ABSTRACT FROM AUTHOR]

Direct regression for the cumulative incidence function (CIF) has become increasingly popular since the Fine and Gray model was suggested (Fine and Gray) due to its more direct interpretation on the probability risk scale. We here consider estimation within the Fine and Gray model using the theory of semiparametric efficient estimation. We show that the Fine and Gray estimator is semiparametrically efficient in the case without censoring. In the case of right-censored data, however, we show that the Fine and Gray estimator is no longer semiparametrically efficient and derive the semiparametrically efficient estimator. This estimation approach involves complicated integral equations, and we therefore also derive a simpler estimator as an augmented version of the Fine and Gray estimator with respect to the censoring nuisance space. While the augmentation term involves the CIF of the competing risk, it also leads to a robustness property: the proposed estimators remain consistent even if one of the models for the censoring mechanism or the CIF of the competing risk are misspecified. We illustrate this robustness property using simulation studies, comparing the Fine–Gray estimator and its augmented version. When the competing cause has a high cumulative incidence we see a substantial gain in efficiency from adding the augmentation term with a very reasonable computation time. for this article are available online. [ABSTRACT FROM AUTHOR]

Aalen's linear hazard rate regression model is a useful and increasingly popular alternative to Cox' multiplicative hazard rate model. It postulates that an individual has hazard rate function h (s) = z 1 α 1 (s) + ⋯ + z r α r (s) in terms of his covariate values z 1 , ... , z r . These are typically levels of various hazard factors, and may also be time-dependent. The hazard factor functions α j (s) are the parameters of the model and are estimated from data. This is traditionally accomplished in a fully nonparametric way. This paper develops methodology for estimating the hazard factor functions when some of them are modelled parametrically while the others are left unspecified. Large-sample results are reached inside this partly parametric, partly nonparametric framework, which also enables us to assess the goodness of fit of the model's parametric components. In addition, these results are used to pinpoint how much precision is gained, using the parametric-nonparametric model, over the standard nonparametric method. A real-data application is included, along with a brief simulation study. [ABSTRACT FROM AUTHOR]

Recurrent events are often encountered in clinical and epidemiological studies where a terminal event is also observed. With recurrent events data it is of great interest to estimate the marginal mean of the cumulative number of recurrent events experienced prior to the terminal event. The standard nonparametric estimator was suggested in Cook and Lawless and further developed in Ghosh and Lin. We here investigate the efficiency of this estimator that, surprisingly, has not been studied before. We rewrite the standard estimator as an inverse probability of censoring weighted estimator. From this representation we derive an efficient augmented estimator using efficient estimation theory for right‐censored data. We show that the standard estimator is efficient in settings with no heterogeneity. In other settings with different sources of heterogeneity, we show theoretically and by simulations that the efficiency can be greatly improved when an efficient augmented estimator based on dynamic predictions is employed, at no extra cost to robustness. The estimators are applied and compared to study the mean number of catheter‐related bloodstream infections in heterogeneous patients with chronic intestinal failure who can possibly die, and the efficiency gain is highlighted in the resulting point‐wise confidence intervals. [ABSTRACT FROM AUTHOR]

For analyzing recurrent event data, we consider a generalization of the classical accelerated failure time model. In the proposed approach, the general function is no longer assumed to be a singleton but allowed to be time-varying. This is in the same spirit as in quantile regression and the counting process techniques can be utilized. Theoretical properties such as consistency and asymptotic normality are obtained. The illustration of the methodology using simulation studies and then the application to the bladder cancer data is also given. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general framework to design accumulation scenarios that can be used to anticipate the impact of a massive cyber attack on an insurance portfolio. The aim is also to emphasize the role of countermeasures in stopping the spread of the attack over the portfolio and to quantify the benefits of implementing such strategies of response. Our approach consists of separating the global dynamic of the cyber event (that can be described through compartmental epidemiological models), the effect on the portfolio, and the response strategy. This general framework allows us to obtain Gaussian approximations for the corresponding processes, and sharp confidence bounds for the losses. A detailed simulation study, which mimics the effects of a Wannacry scenario, illustrates the practical implementation of the method. [ABSTRACT FROM AUTHOR]

In many operations management settings, the arrival process to the system exhibits clear nonstationarities. These nonstationarities may arise as a consequence of time-of-day effects, day-of-week effects, seasonalities, or stochastic fluctuations in the arrival rate. Tools that are developed for performance prediction and decision making when systems are stationary may not be valid in the nonstationary environment. This paper provides a generic, closed-form, and simple approximation tool for when the nonstationarities are caused by rapid fluctuations in the arrival processes. This paper introduces a new asymptotic regime for simplifying stochastic models having nonstationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the arrival process to a service system has an arrival intensity that is fluctuating rapidly. We show that such a service system is well approximated by the corresponding model in which the arrival process is Poisson with a constant arrival rate. In addition to the basic weak convergence theorem, we also establish a first order correction for the distribution of the cumulative number of arrivals over [ 0 , t ] , as well as the number-in-system process for an infinite-server queue fed by an arrival process having a rapidly changing arrival rate. This new asymptotic regime provides a second regime within which nonstationary stochastic models can be reasonably approximated by a process with stationary dynamics, thereby complementing the previously studied setting within which rates vary slowly in time. [ABSTRACT FROM AUTHOR]

Abstract Availability of time series data in different domains has resulted in approaches for outbreak detection. A popular alternative to detect outbreaks is to use daily counts of events. However, time between events (TBE) has proven to be a useful alternative, especially in the case of sudden, unexpected events. Past work that uses TBE for monitoring events assumes that the in‐control number of events is up to 10 per day. In this article, we derive robust monitoring plans that are scalable when the in‐control counts are higher than 10 per day but less than 100 per counting period (eg, day). TBE values are generally nonhomogeneous across days and within days. This makes the volume of data to train the technology a challenge, and this challenge increases the volume of data needed to design the charts. This article discusses these challenges and suggests solutions for data that are known to be Weibull‐distributed. We present our results in two parts. The first is a simulated dataset that controls parameters of the plan such as the daily counts of events. We then show how the monitoring plans can be applied to the detection of syndromes (ie, disease outbreaks) using social media data.

In survival analysis, Cox model is widely used for most clinical trial data. Alternatives include the additive hazard model, the accelerated failure time (AFT) model and a more general transformation model. All these models assume that the effects for all covariates are on the same scale. However, it is possible that for different covariates, the effects are on different scales. In this paper, we propose a shape-invariant hazard regression model that allows us to estimate the multiplicative treatment effect with adjustment of covariates that have non-multiplicative effects. We propose moment-based inference procedures for the regression parameters. We also discuss the risk prediction and the goodness of fit test for our proposed model. Numerical studies show good finite sample performance of our proposed estimator. We applied our method to the HIVNET 012 study, a milestone trial of single-dose nevirapine in prevention of mother-to-child transmission of HIV. From the HIVNET 012 data analysis, single-dose nevirapine treatment is shown to improve 18-month infant survival significantly with appropriate adjustment of the maternal CD4 counts and the virus load. [ABSTRACT FROM AUTHOR]

When applying analysis of variance, the sample sizes may not be previously known, so it is more appropriate to consider them as realizations of random variables. A motivating example is the collection of observations during a fixed time span in a study comparing, for example, several pathologies of patients arriving at a hospital. This paper extends the theory of analysis of variance to those situations considering mixed effects models. We will assume that the occurrences of observations correspond to a counting process and the sample dimensions have Poisson distribution. The proposed approach is applied to a study of cancer patients. [ABSTRACT FROM AUTHOR]

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and typically very challenging to analyze computationally. Recent studies have made progress toward addressing this problem in the context of specific biological systems, but a general and sufficiently effective approach remains lacking. In this work, we propose a mathematical framework based on counting processes that allows us to study dynamic compartment populations with arbitrary interactions and internal biochemistry. We derive an efficient description of the dynamics in terms of differential equations which capture the statistics of the population. We demonstrate the relevance of our approach by analyzing models inspired by different biological processes, including subcellular compartmentalization and tissue homeostasis. [ABSTRACT FROM AUTHOR]

On the basis of Wang and Cheng (J. Math. Anal. Appl. 384 (2011) 597–606), this paper further investigates elementary renewal theorems for counting processes generated by random walks with widely orthant dependent increments. The obtained results improve the corresponding ones of the above-mentioned paper mainly in the sense of weakening the moment conditions on the positive parts of the increments. Meanwhile, a revised version of strong law of large numbers for random walks with widely orthant dependent increments is established, which improves Theorem 1.4 of Wang and Cheng (2011) by enlarging the regions of dominating coefficients. Finally, by using the above results, some precise large deviation results for a nonstandard renewal risk model are established, in which the innovations are widely orthant dependent random variables with common heavy tails, and the inter-arrival times are also widely orthant dependent. [ABSTRACT FROM AUTHOR]

We consider a log-linear model for survival data, where both the location and scale parameters depend on covariates, and the baseline hazard function is completely unspecified. This model provides the flexibility needed to capture many interesting features of survival data at a relatively low cost in model complexity. Estimation procedures are developed, and asymptotic properties of the resulting estimators are derived using empirical process theory. Finally, a resampling procedure is developed to estimate the limiting variances of the estimators. The finite sample properties of the estimators are investigated by way of a simulation study, and a practical application to lung cancer data is illustrated. [ABSTRACT FROM AUTHOR]

Availability of time series data in different domains has resulted in approaches for outbreak detection. A popular alternative to detect outbreaks is to use daily counts of events. However, time between events (TBE) has proven to be a useful alternative, especially in the case of sudden, unexpected events. Past work that uses TBE for monitoring events assumes that the in‐control number of events is up to 10 per day. In this article, we derive robust monitoring plans that are scalable when the in‐control counts are higher than 10 per day but less than 100 per counting period (eg, day). TBE values are generally nonhomogeneous across days and within days. This makes the volume of data to train the technology a challenge, and this challenge increases the volume of data needed to design the charts. This article discusses these challenges and suggests solutions for data that are known to be Weibull‐distributed. We present our results in two parts. The first is a simulated dataset that controls parameters of the plan such as the daily counts of events. We then show how the monitoring plans can be applied to the detection of syndromes (ie, disease outbreaks) using social media data. [ABSTRACT FROM AUTHOR]

Recurrent event data is a special case of multivariate lifetime data that is present in a large variety of studies from numerous disciplines. Due to its pervasiveness, it is essential that appropriate models and inference procedures exist for its analysis. We propose a general class of additive semiparametric models for examining recurrent event data that uses an effective age process to take into account the impact of interventions applied to units after an event occurrence. The effect of covariates is additive instead of the common multiplicative assumption. We derive estimators of the regression parameter, baseline cumulative hazard function, and baseline survival function. We also establish the asymptotic properties of the estimators using tools from empirical process theory. Simulation studies indicate that the asymptotic properties of the regression parameter closely approximate its finite sample properties. The analysis of a real data set consisting of indolent lymphoma recurrence times provides a practical illustration of the class of models and is used to examine the impact of the effective age process. The importance of the effective age process is also demonstrated via the modeling of a data set of failure times for the hydraulic subsystems of load–haul–dump machines used in mining. • A general class of additive semiparametric models for recurrent event data. • Estimators are constructed and their asymptotic properties are established. • Finite sample properties are well approximated by asymptotic properties. • A data set of indolent lymphoma recurrence times is analyzed. [ABSTRACT FROM AUTHOR]

This paper addresses the generalization of counting processes through the age formalism of Lévy Walks. Simple counting processes are introduced and their properties are analyzed: Poisson processes or fractional Poisson processes can be recovered as particular cases. The stationarity assumption in the renewal mechanism characterizing simple counting processes can be modified in different ways, leading to the definition of generalized counting processes. In the case that the transition mechanism of a counting process depends on the environmental conditions—i.e., the parameters describing the occurrence of new events are themselves stochastic processes—the counting processes is said to be influenced by environmental stochasticity. The properties of this class of processes are analyzed, providing several examples and applications and showing the occurrence of new phenomena related to the modulation of the long-term scaling exponent by environmental noise.

The Fleming-Harrington class for right-censored data was first introduced by Harrington and Fleming (1982). This class is widely used in survival analysis studies and it is a subset of the so-called weighted logrank test statistics. Recently, Oller and Gómez (2012) proposed an extension of this class for interval-censored data. This paper introduces the R package FHtest, which implements the Fleming-Harrington class for right-censored and interval-censored survival data. It provides an integrated approach for performing two-sample, k-sample and trend tests based on either counting process theory, likelihood theory, or permutation distributions. In this paper, we summarize the main aspects of the theory framework and present several examples with R codes to illustrate the usage of the main functions of FHtest.

We propose new resampling‐based approaches to construct asymptotically valid time‐simultaneous confidence bands for cumulative hazard functions in multistate Cox models. In particular, we exemplify the methodology in detail for the simple Cox model with time‐dependent covariates, where the data may be subject to independent right‐censoring or left‐truncation. We use simulations to investigate their finite sample behavior. Finally, the methods are utilized to analyze two empirical examples with survival and competing risks data. [ABSTRACT FROM AUTHOR]

Background: Beyond the effort provided on the population policy in Rwanda so far, extensive studies on factors that could prevent infant mortality (IM) should be done for more controlling the Infant mortality rate (IMR). This study presents an application of survival analysis to the infant mortality at the Kigali University Teaching Hospital (KUTH) in Rwanda. Data and methods: The dataset of the KUTH was recorded. Aalen Additive Hazard Model (AAHM) is used for assessing the relationship between the IM and covariates. The Cox Proportional Hazard Model (CPHM) and the Cox-Aalen Hazard Model (CAHM) are also applied, the results of these three models are compared. Findings: The AAHM distinguishes time dependent and fixed covariates, and this allows an easy interpretation of the results found in CPHM and CAHM. Conclusion: Avoidance of pregnancy until after age 20 and clinically recommended nutrition for the mother during pregnancy would decrease IM. [ABSTRACT FROM AUTHOR]

Among Mixed Poisson processes, counting processes having geometrically distributed increments can be obtained when the mixing random intensity is exponentially distributed. Dealing with shock models and compound counting models whose shocks and claims occur according to such counting processes, we provide various comparison results and aging properties concerning total claim amounts and random lifetimes. Furthermore, the main characteristic distributions and properties of these processes are recalled and proved through a direct approach, as an alternative to those available in the literature. We also provide closed-form expressions for the first-crossing-time problem through monotone nonincreasing boundaries, and numerical estimates of first-crossing-time densities through other suitable boundaries. Finally, we present several applications in seismology, software reliability and other fields. [ABSTRACT FROM AUTHOR]

This article focuses on monitor plans aimed at the early detection of the increase in the frequency of events. The literature recommends either monitoring the time between events (TBE) if events are rare or counting the number of events per unit non-overlapping time intervals otherwise. Some authors advocate using the Bernoulli model for rare events, applying presence or absence of events within non-overlapping and exhaustive time intervals. This Bernoulli model does improve the real-time monitoring assessment of these events compared to counting events over a larger interval, making them less rare. However this approach became inefficient if more than one event starts occurring within the intervals. Monitoring TBE is the real-time option for outbreak detection, because outbreak information is accumulated when an event occurs. This is preferred to waiting for the end of a period to count events. If the TBE reduces significantly, then the incidence of these events increases significantly. This article explores this TBE option relative to using the monitoring of counts when the TBEs are either Exponentially, Gamma or Weibull distributed for moderately low count scenarios. The article will discuss and compare the approaches of using an Exponentially Weighted Moving Average (EWMA) statistic for the TBEs to the EWMA of counts. Several robust options will be considered when the future change in event frequency is unknown. Our goal is to have a robust monitoring plan which is able to efficiently detect many different levels of shifts. These robust plans are compared to the more traditional event monitoring plans for both small and large changes in the event frequency. [ABSTRACT FROM AUTHOR]

In studies featuring a sequence of ordered events, gap times between successive events are often of interest. Despite the rich literature in this area, very few methods for comparing gap times have been developed. We propose methods for estimating a hazard ratio connecting the first and second gap times. Specifically, a two-stage procedure is developed based on estimating equations. At the first stage, a proportional hazards model is fitted for the first gap time. Weighted estimating equations are then solved at the second stage to estimate the hazard ratio between the first and second gap times. The proposed estimator has a closed form and, being analogous to a standardized mortality ratio, is easy to interpret. Large sample properties of the proposed estimators are derived, with simulation studies used to evaluate finite sample characteristics. Extension of the approach to accommodate a piecewise constant hazard ratio is considered. The proposed methods are applied to contrast repeat (second) versus primary (first) liver transplants with respect to graft failure, based on national registry data. [ABSTRACT FROM AUTHOR]

Asymptotic properties, both consistency and weak convergence, of estimators arising in a general class of dynamic recurrent event models are presented. The class of models take into account the impact of interventions after each event occurrence, the impact of accumulating event occurrences, the induced informative and dependent right-censoring mechanism due to the data-accrual scheme, and the effect of covariate processes on the recurrent event occurrences. The class of models subsumes as special cases many of the recurrent event models that have been considered in biostatistics, reliability, and in the social sciences. The asymptotic properties presented have the potential of being useful in developing goodness-of-fit and model validation procedures, confidence intervals and confidence bands constructions, and hypothesis testing procedures for the finite- and infinite-dimensional parameters of a general class of dynamic recurrent event models, albeit the models without frailties. [ABSTRACT FROM AUTHOR]

Given a sequence of random variables (rv's) and a real function $$\psi $$ , the $$\psi $$ -exceedances form a subsequence consisting of those rv's larger than a function, $$\psi $$ , of the previous element of the subsequence. We present the basic distribution theory of $$\psi $$ -exceedances for a sequence of independent and identically distributed rv's. We give several examples and we study with more detail the case of exponential parents with $$\psi $$ a linear function. The particular case of arithmetic exceedances is useful to describe the behavior of a type I counter when the arrival process of particles follows a non-homogeneous Poisson process. We also mention applications to destructive testing, early alert systems and the departure process of a $$M_t/D/1/1$$ queue. [ABSTRACT FROM AUTHOR]

We construct a news spreading model with a time dependent contact rate which generalizes the classical Susceptible–Infected model of epidemiology. In particular, we are interested on the time-dynamics of the sharing and diffusion process of news on the Internet. We focus on the counting process describing the number of connections to a given website, characterizing the cumulative density function of its inter-arrival times. Moreover, starting from the general form of the finite dimensional distribution of the process, we determine a formula for the time-variable rate of the connections and establish its relationship with the probability density function of the interarrival times. We finally show the effectiveness of our theoretical framework analyzing a real-world dataset, the Memetracker dataset, whose parameters characterizing the diffusion process are determined. [ABSTRACT FROM AUTHOR]

We consider the problem of learning the inhomogeneous intensity of a counting process, under a sparse segmentation assumption. We introduce a weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We prove that this leads to a sharp tuning of the convex relaxation of the segmentation prior, by stating oracle inequalities with fast rates of convergence, and consistency for change-points detection. This provides first theoretical guarantees for segmentation with a convex proxy beyond the standard independent identically distributed signal + white noise setting. We introduce a fast algorithm to solve this convex problem. Numerical experiments illustrate our approach on simulated and on a high-frequency genomics data set. [ABSTRACT FROM AUTHOR]

A $$\delta $$ -record of a sequence of random variables is an observation that exceeds the current record by $$\delta $$ units. This concept is relatively recent, so there are still many unknown aspects that require further research. In this work, for $$\delta \ge 0$$ , we investigate the distribution theory of $$\delta $$ -record values from an iid sample from an absolutely continuous parent. We obtain recurrent expressions for the density function of $$\delta $$ -records and the probability mass function of inter- $$\delta $$ -record times. In the particular case of the exponential distribution, we show that the sequence of $$\delta $$ -records are distributed as the points of a (delayed) renewal process. Finally, we point out some applications of $$\delta $$ -records to paralyzable counters, blocks in automobile traffic, and queuing theory. [ABSTRACT FROM AUTHOR]

We propose a stochastic semi-Markovian framework for disability modelling in a multi-period discrete-time setting. The logistic transforms of disability inception and recovery probabilities are modelled by means of stochastic risk factors and basis functions, using counting processes and generalized linear models. The model for disability inception also takes IBNR claims into consideration. We fit various versions of the models into Swedish disability claims data. [ABSTRACT FROM PUBLISHER]

In this paper, we propose several approaches to estimate the parameters of the periodic first-order integer-valued autoregressive process with period T (PINAR(1)T) in the presence of missing data. By using incomplete data, we propose two approaches that are based on the conditional expectation and conditional likelihood to estimate the parameters of interest. Then we study three kinds of imputation methods for the missing data. The performances of these approaches are compared via simulations. [ABSTRACT FROM AUTHOR]

In HIV-1 clinical trials the interest is often to compare how well treatments suppress the HIV-1 RNA viral load. The current practice in statistical analysis of such trials is to define a single ad hoc composite event which combines information about both the viral load suppression and the subsequent viral rebound, and then analyze the data using standard univariate survival analysis techniques. The main weakness of this approach is that the results of the analysis can be easily influenced by minor details in the definition of the composite event. We propose a straightforward alternative endpoint based on the probability of being suppressed over time, and suggest that treatment differences be summarized using the restricted mean time a patient spends in the state of viral suppression. A nonparametric analysis is based on methods for multiple endpoint studies. We demonstrate the utility of our analytic strategy using a recent therapeutic trial, in which the protocol specified a primary analysis using a composite endpoint approach. [ABSTRACT FROM AUTHOR]

It is well known that many distributions that arise in the analysis of algorithms have an asymptotically fluctuating behaviour in the sense that we do not have 'full' convergence, but only convergence along suitable subsequences as the size of the input to the algorithm tends to infinity. We are interested in constructions that display such behaviour via an ordinarily convergent background process in the sense that the periodicities arise from this process by deterministic transformations, typically involving discretization as a decisive step. This leads to structural representations of the resulting family of limit distributions along subsequences, which in turn may give access to their properties, such as the tail behaviour (unsuccessful search in digital search trees) or the dependence on parameters of the algorithm (success probability in a selection algorithm).

Multivariate panel count data often occur when there exist several related recurrent events or response variables defined by occurrences of related events. For univariate panel count data, several nonparametric treatment comparison procedures have been developed. However, it does not seem to exist a nonparametric procedure for multivariate cases. Based on differences between estimated mean functions, this article proposes a class of nonparametric test procedures for multivariate panel count data. The asymptotic distribution of the new test statistics is established and a simulation study is conducted. Moreover, the new procedures are applied to a skin cancer problem that motivated this study. [ABSTRACT FROM AUTHOR]

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments (Keiding, 1991; Sun, 2006) and several approaches have been proposed for the additive hazards model with univariate current status data (Lin et al., 1998; Martinussen and Scheike, 2002). For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided. [ABSTRACT FROM AUTHOR]

Abstract: In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics. [Copyright &y& Elsevier]

Abstract: It is shown that, when measuring time in the Total Time on Test scale, the superposition of overlapping realizations of a nonhomogeneous Poisson process is also a Poisson process and is sufficient for inferential purposes. Hence, many nonparametric procedures which are available when only one realization is observed can be easily extended for the overlapping realizations setup. These include, for instance, the constrained maximum likelihood estimator of a monotonic intensity and bootstrap confidence bands based on Kernel estimates of the intensity. The kernel estimate proposed here performs the smoothing in the Total Time on Test scale and it is shown to behave approximately as a usual kernel estimate but with a variable bandwidth which is inversely proportional to the number of realizations at-risk. Likewise, bootstrap samples can be obtained from the single realization of the superimposed process. The methods are illustrated using a real data set consisting of the failure histories of 40 electrical power transformers. [Copyright &y& Elsevier]

Abstract: The field of phylogenetic tree estimation has been dominated by three broad classes of methods: distance-based approaches, parsimony and likelihood-based methods (including maximum likelihood (ML) and Bayesian approaches). Here we introduce two new approaches to tree inference: pairwise likelihood estimation and a distance-based method that estimates the number of substitutions along the paths through the tree. Our results include the derivation of the formulae for the probability that two leaves will be identical at a site given a number of substitutions along the path connecting them. We also derive the posterior probability of the number of substitutions along a path between two sequences. The calculations for the posterior probabilities are exact for group-based, symmetric models of character evolution, but are only approximate for more general models. [Copyright &y& Elsevier]