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This article presents a statistic to identify the proportional intensity of an area to belong to a space-time cluster, which is very important in spatial statistics. A significant extension of the so-called F -function has been described in detail, which, associated with new technology, allows the evaluation of the intensity of change moments in the time process and outline possible occurrences of clusters. The justification of the study is performed through an extensive review of the current literature of the area. The developed algorithms are detailed via computational experiments with simulated data. Real situations are presented and discussed in detail. Finally, topics for future research are indicated. [ABSTRACT FROM AUTHOR]

This work is a simulation study to investigate the sensitivity of multivariate control charts for monitoring mean vectors in a bivariate Gaussian process with individual observations. The multivariate cumulative sum (MCUSUM), the multivariate exponentially weighted moving average (MEWMA) and Hotelling's T charts are selected for analysis due to their common dependency on the non-centrality parameter. The chart performance is evaluated through the average run length (ARL) or the average time to signal. The impact of utilising in-control limits computed from known parameters or Phase I sample estimates is considered for mean vector shifts. Although designed to monitor mean vectors, the sensibility of the control charts is additionally analysed through different variability sources, including the mixing effect of mean vector shifts with increasing variances or positive autocorrelation in the out-of-control process. [ABSTRACT FROM AUTHOR]

In this paper, a multivariate log‐Weibull model for spatially dependent data is defined by marginalizing a conditional Pareto distribution with respect to a shared spatial random effect of alpha‐stable distributions. Some properties of this new model are derived, and procedures for the estimation and inference are discussed. An application is developed to study observed temperature data sets collected from weather stations in the Brazilian Amazon. [ABSTRACT FROM AUTHOR]