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Research Project
Centre of Statistics and its Applications
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Publications
Approximating the distribution of the product of two normally distributed random variables
Publication . Seijas-Macias, J. Antonio; Oliveira, Amilcar; Oliveira, Teresa A.; Leiva, Victor
The distribution of the product of two normally distributed random variables has been an
open problem from the early years in the XXth century. First approaches tried to determinate the
mathematical and statistical properties of the distribution of such a product using different types of
functions. Recently, an improvement in computational techniques has performed new approaches
for calculating related integrals by using numerical integration. Another approach is to adopt any
other distribution to approximate the probability density function of this product. The skew-normal
distribution is a generalization of the normal distribution which considers skewness making it flexible.
In this work, we approximate the distribution of the product of two normally distributed random
variables using a type of skew-normal distribution. The influence of the parameters of the two normal
distributions on the approximation is explored. When one of the normally distributed variables has
an inverse coefficient of variation greater than one, our approximation performs better than when
both normally distributed variables have inverse coefficients of variation less than one. A graphical
analysis visually shows the superiority of our approach in relation to other approaches proposed in
the literature on the topic.
A strategy to assess water meter performance
Publication . Cordeiro, Clara; Borges, Ana; Ramos, Maria do Rosário
Apparent water losses can be problematic to water companies’ revenues. This type of loss is very difficult to detect and quantify and is often associated with water meter anomalies. This study was motivated by a water company’s challenge that links a decrease in water consumption to water meters’ malfunction. The aim is to develop a strategy to detect decreasing water usage patterns, contributing to meter performance assessment. The basis of the approach is a combination of statistical methods. First, the time series of billed water consumption is decomposed using Seasonal-Trend decomposition based on Loess. Next, breakpoint analysis is performed on the seasonally adjusted time series. After that, the Mann–Kendall test and Sen’s slope estimator are used to analyze periods of progressive decrease changes in water consumption, defined by breakpoints. A quantitative indicator of this change is proposed. The strategy was successfully applied to eight-time series of water consumption from the Algarve, Portugal.
Big data sets in environmental studies
Publication . Oliveira, Amilcar
Big Data datasets for environmental studies play a crucial role in understanding, monitoring and addressing large-scale environmental issues. Big Data datasets for environmental studies deal with huge volumes of data coming from various sources such as satellites, remote sensors, weather stations, sensor networks and mobile devices. These datasets include detailed information on climate change, biodiversity, air quality, water resources and other environmental parameters. Integrating and analyzing data from different sources allows for a more comprehensive understanding of environmental standards and helps in making informed decisions. The generation of environmental data occurs in real time, especially with the increased use of sensors and continuous monitoring technologies. The ability to handle the velocity of data is essential for detecting rapid changes in the environment and responding to critical events such as natural disasters. Predictive models help predict climate patterns, identify areas of environmental risk and assess the impacts of human activities on the ecosystem. This data is crucial for developing mitigation strategies, adapting to climate change and conserving biodiversity. In summary, Big Data datasets play a fundamental role in environmental studies, providing a comprehensive and real-time understanding of environmental challenges, enabling the implementation of effective strategies for conservation and sustainability.
Analysis of the inequality into distributions: an alternative approach to the Gini index applied to the spending environmental in EU
Publication . Seijas-Macias, Antonio; Oliveira, Amilcar; Oliveira, Teresa A.
The Gini index is the most common tool to measure inequality into two distributions. Traditionally, the Gini index and the curve of Lorenz are focused on inequalities measures in the income distribution between countries or regions. But, in the last years, several authors have shown some limitations of the Gini index. In particular, it’s less sensitive to inequality at the tail of income distribution. This type of problem in the Gini index could produce two types of reactions: a new reinterpretation of the Gini index and the proposal of some alternative measures to it. In this paper, we follow the previous work using the Csiszar f-divergence to propose using the α-divergences approach to analyze the differences between the Gini index approach and these alternatives. The Gini index has been applied to the measure of resource inequalities. The AR-Gini is an area-based measure of resource inequality that estimates inequalities between neighbourhoods regarding the consumption of specific consumer goods (Druckman and Jackson, 2008). The AR-Gini could be a useful tool to monitor the distributional impacts of resource-related interventions, but this indicator presents the same overcomes as the Gini index. We can use the Gini concentration coefficient as a measure of the concentration of distribution of a random variable, especially applied to time series of data. In recent years, several studies have studied environmental spending in the European Union (EU). We focus our analysis on the distribution of this type of spending between the countries of the EU.
The objective of this study is to show the differences in indexes applied to the study of the distribution of the distribution of monetary resources to environmental conservation and the extension of environmental protected areas into the countries of the European Union (EU). In our comparative study, we use the Gini index and the α-divergence measure and compare the results to get the most accurate measure of the equity of the distribution.
Uncovering abnormal water consumption patterns for sustainability’s sake: a statistical approach
Publication . Borges, Ana; Cordeiro, Clara; Ramos, Maria do Rosário
Monitoring domestic water usage may help the water utilities uncover abnormal water consumption. In this context, it is necessary to improve and develop tools based on data analysis of households’ meter readings. This study contributes to this goal by using a statistical methodology that detects abnormal water consumption patterns, namely, significant increases or decreases. This approach relies on a combination of methods that analyse billed water consumption time series. The first step is to decompose the time series using Seasonal-Trend decomposition based on Loess. Next, breakpoint analysis is performed on the seasonally adjusted time series to look for changes in the pattern over time. Afterwards, the Mann–Kendall test and Sen’s slope estimator are applied to assess whether there are significant increases or decreases in water consumption. The strategy is applied to water consumption data from the Algarve, Portugal, successfully detecting breakpoints associated with significant increasing or decreasing trends.
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Funders
Funding agency
Fundação para a Ciência e a Tecnologia
Funding programme
6817 - DCRRNI ID
Funding Award Number
UIDB/00006/2020