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AbstractIn recent three decades, there has been a rapid increasing interest in the mixture models for ordinal responses, and the classical CUB model as a fundamental one has been extended to different preference and uncertainty models. In this article, based on a response style supported by Zipf’s law, we propose a novel mixture model for ordinal responses via replacing the uncertainty component of the CUB model with a truncated Zeta distribution. Parameters estimation with EM algorithm, inferential issues with respect to the approximation of a truncated Riemann Zeta function and estimators’ variance-covariance information matrix are investigated. The advantages of the proposed model over the CUB model have been illustrated with simulations of two sets of Monte Carlo experiments and practical applications of a health survey and a bicycle use. The intention of the article is to distinguish the respondents’ true preference from the response style of “the higher, the less”, so as to understand more reasonably the formation causes of ordinal responses. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonparametric Shewhart chart for fuzzy data. We utilize the fuzzy data without transforming them into a real-valued scalar (a representative value). Usually fuzzy data (described by fuzzy random variables) do not have a distributional model available, and also the size of the fuzzy sample data is small. Based on the bootstrap methodology, we design a nonparametric Shewhart control chart in the space of fuzzy random variables equipped with some L2 metric, in which a novel approach for generating the control limits is proposed. The control limits are determined by the necessity index of strict dominance combined with the bootstrap quantile of the test statistic. An in-control bootstrap ARL of the proposed chart is also considered.

We consider a novel univariate non parametric cumulative sum (CUSUM) control chart for detecting the small shifts in the mean of a process, where the nominal value of the mean is unknown but some historical data are available. This chart is established based on the Mann–Whitney statistic as well as the change-point model, where any assumption for the underlying distribution of the process is not required. The performance comparisons based on simulations show that the proposed control chart is slightly more effective than some other related non parametric control charts. [ABSTRACT FROM AUTHOR]

Some asymptotic properties of point estimation with n -dimensional fuzzy data with respect to a special L 2 -metric ρ are investigated in this article. It is shown that the collection of all n -dimensional fuzzy data endowed with the ρ-metric is a complete and separable space. Some criterions for point estimation in such fuzzy environments are proposed, and the sample mean, variance and covariance with n -dimensional fuzzy data under these criteria are further studied. [ABSTRACT FROM AUTHOR]