Balanced e-optimal designs of resolution III for the 2×3 series

We consider the problem of constructing designs which are E-optimal in the class of all balanced resolution III designs for the 2^m×3ⁿ series. The inverse of the information matrix for general resolution III balanced 2^m×3ⁿ designs is obtained. Optimal designs are constructed for the cases (m,n)=(3, 1), (4, 1), (2, 2) and (3, 2) for various numbers of runs in the practical range.     

Richness orderings

An index of richness in a society is a measure of the extent of its affluence. This paper presents an analytical discussion on several indices of richness and their properties. It also develops criteria for ordering alternative distributions of income in terms of their richness. Given a line of richness, an income level above which a person is regarded as rich, and depending on the redistributive principle, it is shown that the ranking relation can be implemented by seeking dominance with respect to the generalized Lorenz curve of the rich or the affluence profile of the society. When the line of richness is assumed to be variable, we need to employ the stochastic dominance conditions for ordering the income distributions.     

Pfeifer records process

In this article, we study the limit distribution of sums of Pfeifer records. Motivated by the results obtained by Arnold and Villaseñor [Generalized order statistics process and Pfeifer records, Statistics 46(3) (2012), pp. 373–385], we show that the partial sum process of Pfeifer records converge to a function of the Brownian motion. The normalization is either a sequence of appropriate constants or a sequence of functions, depending on the tail behaviour of the underlying variables. These results, in particular, prove stronger version of results obtained in Villaseñor and Arnold [On limit laws for sums of Pfeifer records, Extremes 10 (2007), pp. 235–248] and Bose and Gangopadhyay [Convergence of linear functions of Pfeifer records, Extremes 13 (2010), pp. 89–106] and extends results of Bose et al. [Partial sum process for records, Extremes 8 (2005), pp. 43–56] from classical records to Pfeifer records.     

Admissibility in factorial designs

The notion of admissibility in factorial designs has been introduced. It has been shown that factorial designs which are binary and have a C-matrix with property A are admissible.     

Modeling Bimodal Discrete Data Using Conway-Maxwell-Poisson Mixture Models

Bimodal truncated count distributions are frequently observed in aggregate survey data and in user ratings when respondents are mixed in their opinion. They also arise in censored count data, where the highest category might create an additional mode. Modeling bimodal behavior in discrete data is useful for various purposes, from comparing shapes of different samples (or survey questions) to predicting future ratings by new raters. The Poisson distribution is the most common distribution for fitting count data and can be modified to achieve mixtures of truncated Poisson distributions. However, it is suitable only for modeling equidispersed distributions and is limited in its ability to capture bimodality. The Conway–Maxwell–Poisson (CMP) distribution is a two-parameter generalization of the Poisson distribution that allows for over- and underdispersion. In this work, we propose a mixture of CMPs for capturing a wide range of truncated discrete data, which can exhibit unimodal and bimodal behavior. We present methods for estimating the parameters of a mixture of two CMP distributions using an EM approach. Our approach introduces a special two-step optimization within the M step to estimate multiple parameters. We examine computational and theoretical issues. The methods are illustrated for modeling ordered rating data as well as truncated count data, using simulated and real examples.     

A law of large numbers for the scaled age distribution of linear birth-and-death processes

It is shown that certain measure-valued stochastic processes describing the age distribution of particles whose development is controlled by linear critical birth-and-death processes converge in distribution to a deterministic positive bounded measure.     

Privacy protection measures for randomized response surveys on stigmatizing continuous variables

We consider the situation where sample surveys are to be undertaken on sensitive or stigmatizing issues. For such surveys, direct questioning methods usually lead to non-compliance or incorrect responses and so, the randomized response technique, where the responses are collected through some randomization device, is found to be useful. A majority of the literature on these techniques focus on dichotomous sensitive variables, while some techniques are also available for continuous sensitive variables. In this article, we focus on the extent of privacy protection available in sample surveys to respondents for continuous response variables. We also propose two measures of privacy protection. We demonstrate that the parameters of our randomization scheme can be so chosen as to achieve a pre-assigned level of privacy protection while at the same time yielding efficient estimates. We also show some numerical comparisons.     

A Fuzzy‐Based Risk Assessment Framework for Autonomous Underwater Vehicle Under‐Ice Missions

The use of autonomous underwater vehicles (AUVs) for various scientific, commercial, and military applications has become more common with maturing technology and improved accessibility. One relatively new development lies in the use of AUVs for under‐ice marine science research in the Antarctic. The extreme environment, ice cover, and inaccessibility as compared to open‐water missions can result in a higher risk of loss. Therefore, having an effective assessment of risks before undertaking any Antarctic under‐ice missions is crucial to ensure an AUV's survival. Existing risk assessment approaches predominantly focused on the use of historical fault log data of an AUV and elicitation of experts’ opinions for probabilistic quantification. However, an AUV program in its early phases lacks historical data and any assessment of risk may be vague and ambiguous. In this article, a fuzzy‐based risk assessment framework is proposed for quantifying the risk of AUV loss under ice. The framework uses the knowledge, prior experience of available subject matter experts, and the widely used semiquantitative risk assessment matrix, albeit in a new form. A well‐developed example based on an upcoming mission by an ISE‐explorer class AUV is presented to demonstrate the application and effectiveness of the proposed framework. The example demonstrates that the proposed fuzzy‐based risk assessment framework is pragmatically useful for future under‐ice AUV deployments. Sensitivity analysis demonstrates the validity of the proposed method.