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In this paper, a robust analysis of SO2 concentration measurements taken at the Belisario air quality monitoring station, Quito, Ecuador is carried out. The analyzed data contain 12 years of measurements, from January 2008 to December 2019. In addition, this set of measurements was decomposed into variables that represent each year, month, day of the week, and hour of the day in groups of two hours. For the analysis, classic, nonparametric and robust statistical methods were used, and the data were classified based on criteria established by the Quiteño Air Quality Index, taking confidence intervals into account. The results showed that the level of air pollution at the Belisario station due to the SO2 concentration is acceptable. In addition, the trend in the level of SO2 concentration decreased over the years studied, with a sharp drop from 2008 to 2012, then a small rise in 2013 and another fall until 2019, presenting decreasing oscillations that tend toward a desirable level of pollution. In this paper, it was shown that the air pollution at the Belisario station due to the concentration of SO2 in the last 12 years is not harmful to humans, with the measurement precision provided by robust statistical methods. Therefore, it can be concluded that the measures that have been taken by the Quito city council over the last few years are yielding good results.

In this paper, a robust analysis of nitrogen dioxide (NO2) concentration measurements taken at Belisario station (Quito, Ecuador) was performed. The data used for the analysis constitute a set of measurements taken from 1 January 2008 to 31 December 2019. Furthermore, the analysis was carried out in a robust way, defining variables that represent years, months, days and hours, and classifying these variables based on estimates of the central tendency and dispersion of the data. The estimators used here were classic, nonparametric, based on a bootstrap method, and robust. Additionally, confidence intervals based on these estimators were built, and these intervals were used to categorize the variables under study. The results of this research showed that the NO2 concentration at Belisario station is not harmful to humans. Moreover, it was shown that this concentration tends to be stable across the years, changes slightly during the days of the week, and varies greatly when analyzed by months and hours of the day. Here, the precision provided by both nonparametric and robust statistical methods served to comprehensively proof the aforementioned. Finally, it can be concluded that the city of Quito is progressing on the right path in terms of improving air quality, because it has been shown that there is a decreasing tendency in the NO2 concentration across the years. In addition, according to the Quito Air Quality Index, most of the observations are in either the desirable level or acceptable level of air pollution, and the number of observations that are in the desirable level of air pollution increases across the years.

This paper presents a robust analysis of carbon monoxide (CO) concentration measurements conducted at the Belisario air-quality monitoring station (Quito, Ecuador). For the analysis, the data collected from 1 January 2008 to 31 December 2019 were considered. Additionally, each of the twelve years analyzed was considered as a random variable, and robust location and scale estimators were used to estimate the central tendency and dispersion of the data. Furthermore, classic, nonparametric, bootstrap, and robust confidence intervals were used to group the variables into categories. Then, differences between categories were quantified using confidence intervals and it was shown that the trend of CO concentration at the Belisario station in the last twelve years is downward. The latter was proven with the precision provided by both nonparametric and robust statistical methods. The results of the research work robustly proved that the CO concentration at Belisario station in the last twelve years is not considered a health risk, according to the criteria established by the Quito Air Quality Index.

Various confidence interval estimators have been developed for differences in proportions resulted from correlated binary data. However, the width of the mostly recommended Tango's score confidence interval tends to be wide, and the computing burden of exact methods recommended for small-sample data is intensive. The recently proposed rank-based nonparametric method by treating proportion as special areas under receiver operating characteristic provided a new way to construct the confidence interval for proportion difference on paired data, while the complex computation limits its application in practice. In this article, we develop a new nonparametric method utilizing the U-statistics approach for comparing two or more correlated areas under receiver operating characteristics. The new confidence interval has a simple analytic form with a new estimate of the degrees of freedom of n - 1. It demonstrates good coverage properties and has shorter confidence interval widths than that of Tango. This new confidence interval with the new estimate of degrees of freedom also leads to coverage probabilities that are an improvement on the rank-based nonparametric confidence interval. Comparing with the approximate exact unconditional method, the nonparametric confidence interval demonstrates good coverage properties even in small samples, and yet they are very easy to implement computationally. This nonparametric procedure is evaluated using simulation studies and illustrated with three real examples. The simplified nonparametric confidence interval is an appealing choice in practice for its ease of use and good performance. [ABSTRACT FROM AUTHOR]

Quantiles, which are also known as values-at-risk in finance, frequently arise in practice as measures of risk. Confidence intervals for quantiles are typically constructed via large sample theory or the sectioning. One of the ways for achieving the confidence interval for quantiles is direct use of a central limit theorem. In this approach, we require a good estimator of the quantile density function. In this paper, we consider the nonparametric estimator of the quantile density function from Soni et al. (2012) and we obtain confidence interval for quantiles. In the following, by using simulation, the coverage probability and mean square error of this confidence interval is calculated. Also, we compare our proposed approach with alternative approaches such as sectioning and jackknife [ABSTRACT FROM AUTHOR]

The average availability of a repairable system is the expected proportion of time that the system is operating in the interval [0, t]. The present article discusses the nonparametric estimation of the average availability when (i) the data on 'n' complete cycles of system operation are available, (ii) the data are subject to right censorship, and (iii) the process is observed upto a specified time 'T'. In each case, a nonparametric confidence interval for the average availability is also constructed. Simulations are conducted to assess the performance of the estimators. [ABSTRACT FROM AUTHOR]

In this paper, a robust analysis of nitrogen dioxide (NO2) concentration measurements taken at Belisario station (Quito, Ecuador) was performed. The data used for the analysis constitute a set of measurements taken from 1 January 2008 to 31 December 2019. Furthermore, the analysis was carried out in a robust way, defining variables that represent years, months, days and hours, and classifying these variables based on estimates of the central tendency and dispersion of the data. The estimators used here were classic, nonparametric, based on a bootstrap method, and robust. Additionally, confidence intervals based on these estimators were built, and these intervals were used to categorize the variables under study. The results of this research showed that the NO2 concentration at Belisario station is not harmful to humans. Moreover, it was shown that this concentration tends to be stable across the years, changes slightly during the days of the week, and varies greatly when analyzed by months and hours of the day. Here, the precision provided by both nonparametric and robust statistical methods served to comprehensively proof the aforementioned. Finally, it can be concluded that the city of Quito is progressing on the right path in terms of improving air quality, because it has been shown that there is a decreasing tendency in the NO2 concentration across the years. In addition, according to the Quito Air Quality Index, most of the observations are in either the desirable level or acceptable level of air pollution, and the number of observations that are in the desirable level of air pollution increases across the years. [ABSTRACT FROM AUTHOR]

This paper presents a robust analysis of carbon monoxide (CO) concentration measurements conducted at the Belisario air-quality monitoring station (Quito, Ecuador). For the analysis, the data collected from 1 January 2008 to 31 December 2019 were considered. Additionally, each of the twelve years analyzed was considered as a random variable, and robust location and scale estimators were used to estimate the central tendency and dispersion of the data. Furthermore, classic, nonparametric, bootstrap, and robust confidence intervals were used to group the variables into categories. Then, differences between categories were quantified using confidence intervals and it was shown that the trend of CO concentration at the Belisario station in the last twelve years is downward. The latter was proven with the precision provided by both nonparametric and robust statistical methods. The results of the research work robustly proved that the CO concentration at Belisario station in the last twelve years is not considered a health risk, according to the criteria established by the Quito Air Quality Index. [ABSTRACT FROM AUTHOR]