Statistical analysis for competing risks model from a Weibull distribution under progressively hybrid censoring

This paper considers the statistical analysis for competing risks model under the Type-I progressively hybrid censoring from a Weibull distribution. We derive the maximum likelihood estimates and the approximate maximum likelihood estimates of the unknown parameters. We then use the bootstrap method to construct the confidence intervals. Based on the non informative prior, a sampling algorithm using the acceptance–rejection sampling method is presented to obtain the Bayes estimates, and Monte Carlo method is employed to construct the highest posterior density credible intervals. The simulation results are provided to show the effectiveness of all the methods discussed here and one data set is analyzed.     

Two-Piece location-scale distributions based on scale mixtures of normal family

In this work, we study the maximum likelihood (ML) estimation problem for the parameters of the two-piece (TP) distribution based on the scale mixtures of normal (SMN) distributions. This is a family of skewed distributions that also includes the scales mixtures of normal class, and is flexible enough for modeling symmetric and asymmetric data. The ML estimates of the proposed model parameters are obtained via an expectation-maximization (EM)-type algorithm.     

Time series analysis of categorical data using auto-mutual information

Despite its importance, there has been little attention in the modeling of time series data of categorical nature in the recent past. In this paper, we present a framework based on the Pegram's [An autoregressive model for multilag Markov chains. Journal of Applied Probabability 17, 350–362] operator that was originally proposed only to construct discrete AR(p$p$) processes. We extend the Pegram's operator to accommodate categorical processes with ARMA representations. We observe that the concept of correlation is not always suitable for categorical data. As a sensible alternative, we use the concept of mutual information, and introduce auto-mutual information to define the time series process of categorical data. Some model selection and inferential aspects are also discussed. We implement the developed methodologies to analyze a time series data set on infant sleep status.     

Blind nonparametric regression

One must sometimes follow the evolution of several individuals which cannot be distinguished. The author proposes a graphical estimator of individual evolution that can be used in such cases. She shows that this estimator is consistent and asymptotically normal.     

Score estimation in the monotone single‐index model

We consider estimation in the single‐index model where the link function is monotone. For this model, a profile least‐squares estimator has been proposed to estimate the unknown link function and index. Although it is natural to propose this procedure, it is still unknown whether it produces index estimates that converge at the parametric rate. We show that this holds if we solve a score equation corresponding to this least‐squares problem. Using a Lagrangian formulation, we show how one can solve this score equation without any reparametrization. This makes it easy to solve the score equations in high dimensions. We also compare our method with the effective dimension reduction and the penalized least‐squares estimator methods, both available on CRAN as R packages, and compare with link‐free methods, where the covariates are elliptically symmetric.     

Research Synthesis Methods in an Age of Globalized Risks: Lessons from the Global Burden of Foodborne Disease Expert Elicitation

We live in an age that increasingly calls for national or regional management of global risks. This article discusses the contributions that expert elicitation can bring to efforts to manage global risks and identifies challenges faced in conducting expert elicitation at this scale. In doing so it draws on lessons learned from conducting an expert elicitation as part of the World Health Organizations (WHO) initiative to estimate the global burden of foodborne disease; a study commissioned by the Foodborne Disease Epidemiology Reference Group (FERG). Expert elicitation is designed to fill gaps in data and research using structured, transparent methods. Such gaps are a significant challenge for global risk modeling. Experience with the WHO FERG expert elicitation shows that it is feasible to conduct an expert elicitation at a global scale, but that challenges do arise, including: defining an informative, yet feasible geographical structure for the elicitation; defining what constitutes expertise in a global setting; structuring international, multidisciplinary expert panels; and managing demands on experts’ time in the elicitation. This article was written as part of a workshop, “Methods for Research Synthesis: A Cross‐Disciplinary Approach” held at the Harvard Center for Risk Analysis on October 13, 2013.     

Public Understanding of Ebola Risks: Mastering an Unfamiliar Threat

Ebola was the most widely followed news story in the United States in October 2014. Here, we ask what members of the U.S. public learned about the disease, given the often chaotic media environment. Early in 2015, we surveyed a representative sample of 3,447 U.S. residents about their Ebola‐related beliefs, attitudes, and behaviors. Where possible, we elicited judgments in terms sufficiently precise to allow comparing them to scientific estimates (e.g., the death toll to date and the probability of dying once ill). Respondents’ judgments were generally consistent with one another, with scientific knowledge, and with their self‐reported behavioral responses and policy preferences. Thus, by the time the threat appeared to have subsided in the United States, members of the public, as a whole, had seemingly mastered its basic contours. Moreover, they could express their beliefs in quantitative terms. Judgments of personal risk were weakly and inconsistently related to reported gender, age, education, income, or political ideology. Better educated and wealthier respondents saw population risks as lower; females saw them as higher. More politically conservative respondents saw Ebola as more transmissible and expressed less support for public health policies. In general, respondents supported providing “honest, accurate information, even if that information worried people.” These results suggest the value of proactive communications designed to inform the lay public's decisions, thoughts, and emotions, and informed by concurrent surveys of their responses and needs.     

Generalized Weighted Exponential Distribution

The new class of weighted exponential (WE) distributions obtained by Gupta and Kundu (2009) by implementing Azzalini's method to the exponential distribution. In this study, we generalize the WE distribution to a new class of generalized weighted exponential (GWE) distribution. Several statistical and reliability properties of this new class of distribution are obtained. Estimation and inference procedure for distribution parameters are investigated. Finally, we show that the proposed model can provide better fit than the recent class of weighted exponential by using two real data examples.     

Inference for Burr XII distribution under Type I progressive hybrid censoring

We consider estimation of unknown parameters of a Burr XII distribution based on progressively Type I hybrid censored data. The maximum likelihood estimates are obtained using an expectation maximization algorithm. Asymptotic interval estimates are constructed from the Fisher information matrix. We obtain Bayes estimates under the squared error loss function using the Lindley method and Metropolis–Hastings algorithm. The predictive estimates of censored observations are obtained and the corresponding prediction intervals are also constructed. We compare the performance of the different methods using simulations. Two real datasets have been analyzed for illustrative purposes.     

Queue Length Analysis of MAP/G/1 Queue Under D-Policy

Abstract

We study the queue length distribution of a queueing system with MAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths will be derived from these transform results. A numerical example is provided.