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The importance of urban water supply systems and public services is globally recognized. Nonrevenue water directly affects a water utility's economic, financial, and environmental sustainability. In Portugal, the mean of the nonrevenue water for the distribution systems corresponded to 28.8% in 2019. Smart metering technology is crucial for consumption monitoring and enhancing apparent and real loss network management (e.g., water meters' global error evaluation, detection of illegal uses, and real loss estimation through the minimum night flow analysis). However, this technology is expensive in acquisition, installation, operation, and maintenance. This study aims to support water utilities in inferring the total consumption using a representative sample of customers with smart meters instead of smart metering data from all customers. A stratified sampling was considered using only the customers' billing time series for the strata definition. A predominantly domestic zone was used, and eight strata were obtained with a clustering analysis [temporal correlation (CORT) dissimilarity and Ward method]. Stratified sampling was applied to minimize the variance of the total water consumption estimator. A representative sample of 259 dimensions (53%) was chosen to infer, with small errors, essential consumption statistics for water utilities: total consumption (with an error of 0.12%), total consumption time series, water consumption patterns, minimum night consumption, and volume distribution by the flow rate. The successful outcomes obtained were crucial in supporting the proposed methodology. This study has provided evidence that installing smart meters for all consumers in a distribution network area is not necessary to acquire accurate and meaningful consumption information crucial for effective network management and water loss control. Moreover, using only billing data to perform the sample selection of consumers is useful for water utilities, because they may face difficulties obtaining extra consumer information. [ABSTRACT FROM AUTHOR]

In this paper we propose an new approach to multivariate collective models based on asymptotic distibutions, since the modeling problems posed have large samples. Collective risk models play an important part in Risk Theory and in Actuarial Mathematics. Inference based on these models is centered on claims totals. However, the new approach has in mind a different kind of risk, the risk of forest fires, where the variables of interest are the number fires and the total burnt areas. As a result, a special case bivariate risk model is derived with this intent. Besides single models, structured families whose models correspond to the treatments of a base linear model are considered. This leads to an ANOVA-like situation where we don't have to estimate the error, which enable to test the influence of several factors on the multivariate collective models mean vectors. Instead of F tests, we use χ 2 tests, availing us of asymptotic distributions that lightens the treatment. To illustrate the approach, an application to forest fires in Portugal with real data is presented. [ABSTRACT FROM AUTHOR]