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Given two continuous random variables, X and Y, we study the relationship between their statistical dependence and the Young tableau of the permutation defined from the graph of a bivariate sample coming from (X, Y). From a sample of size n of (X, Y), we identify the Young tableau of the permutation which maps the ranks of the X observations on the ranks of the Y observations. Procedures to detect statistical dependence between pairs of random variables, based on statistics calculated on the permutation defined by the graph of a bivariate sample have been developed, see García and González-López (2020) [Symmetry 12, 9, 1415. https://doi.org/10.3390/sym12091415] and García and González-López (2014) [J Multivar Anal 127, 126–146. https://doi.org/10.1016/j.jmva.2014.02.010]. In those papers, the information used is the length of the longest increasing (decreasing) subsequence, identified as the first line (the first column) of the Young tableau of the permutation. In this paper, we expose the information captured by the shape of the Young tableau of the permutation.

In this paper, we introduce a method to construct copulas. The method is based on combining the partial derivatives of two copulas. We prove that the proposed method provides a copula. Then, we exemplify the application of the method in several cases, illustrating the versatility of the method. We also prove that using copulas from the family introduced in Rodríguez-Lallena and Úbeda-Flores (2004) [Stat Probab Lett 66, 3, 315–325. https://doi.org/10.1016/j.spl.2003.09.010], the method provides a copula inside that family.

In this article, we define consumers’ profiles of electricity who commit fraud. We also compare these profiles with users’ profiles not classified as fraudsters in order to determine which of these clients should receive an inspection. We present a statistically consistent method to classify clients/users as fraudsters or not, according to the profiles of previously identified fraudsters. We show that it is possible to use several characteristics to inspect the classification of fraud; those aspects are represented by the coding performed in the observed series of clients/users. In this way, several encodings can be used, and the client risk can be constructed to integrate complementary aspects. We show that the classification method has success rates that exceed 77%, which allows us to infer confidence in the methodology.

In this paper, we combine two statistical tools with the objective of creating models that represent the dependence between (i) the proportion of the black/brown population in relation to the total population of a neighborhood (pct) and (ii) the average age at which people died in the neighborhood (age). We explore the dependence between pct and age in São Paulo city, Brazil, during 2018. The statistical tools are models of copulas and informative and non-informative settings according to the Bayesian perspective. The different scenarios and models allow us to delineate the dependence between pct and age, and, through the Bayesian Information Criterion we can indicate which of these models best represents the data. The approach implemented here allows us to define estimates of variations in life expectancy conditioned by percentage intervals of pct. With them, we can conclude that on average all the scenarios point to a decrease in life expectancy by increasing the proportion of pct. When conditioning the percentages of pct to 4 intervals (0, 0.25], (0.25, 0.5], (0.5, 0.75], (0.75, 1] respectively, we note that the expectation is reduced in average at a constant rate from one interval in comparison with the immediate and next interval from left to right in [0, 1].

In this article, we model the dependence between dam factor and D max, where dam factor is an indicator of risk of a tailings dam failure, which involves the height H of the tailings dam, the volume of material housed by the tailings dam VT and the volume dispensed by the tailings dam, VF, when the dam breaks. And, Dmax is the maximum distance traveled by the material released by the tailings dam, after the collapse. With the dependence found via copula models and Bayesian estimation, given a range of dam factor, we estimate the probability of the released material to exceed a certain threshold. Since the dam factor involves the released volume VF (unknown before the dam break), we present a naive way to estimate it using VT and H. In this way, it is possible to estimate the dam factor of a tailings dam and with such a value to identify the probability of the tailings dam to show a Dmax that exceeds a certain threshold.

In this paper, we investigate a specific structure within the theoretical framework of Partition Markov Models (PMM) [see García Jesús and González-López, Entropy 19, 160 (2017)]. The structure of interest lies in the formulation of the underlying partition, which defines the process, in which, in addition to a finite memory o associated with the process, a parameter G is introduced, allowing an extra dependence on the past complementing the dependence given by the usual memory o. We show, by simulations, how algorithms designed for the classic version of the PMM can have difficulties in recovering the structure investigated here. This specific structure is efficient for modeling a complete genome sequence, coming from the newly decoded Coronavirus Covid-19 in humans [see Wu et al., Nature 579, 265–269 (2020)]. The sequence profile is represented by 13 units (parts of the state space’s partition), for each of the 13 units, their respective transition probabilities are computed for any element of the genetic alphabet. Also, the structure proposed here allows us to develop a comparison study with other genomic sequences of Coronavirus, collected in the last 25 years, through which we conclude that Covid-19 is shown next to SARS-like Coronaviruses (SL-CoVs) from bats specimens in Zhoushan [see Hu et al., Emerg Microb Infect 7, 1–10 (2018)].

We build a profile of the Epstein-Barr virus (EBV) by means of genomic sequences obtained from patients with nasopharyngeal carcinoma (NPC). We consider a set of sequences coming from the NCBI free source and we assume that this set is a collection of independent samples of stochastic processes related by an equivalence relation. Given a collection {(Xjt)t∈ℤ}pj=1 { ( X t j ) t ∈ Z } j = 1 p $ \{({X}_t^j{)}_{t\in \mathbb{Z}}{\}}_{j=1}^p$ of p independent discrete time Markov processes with finite alphabet A and state space S, we state that the elements (i, s) and (j, r) in {1, 2,…, p} × S are equivalent if and only if they share the same transition probability for all the elements in the alphabet. The equivalence allows to reduce the number of parameters to be estimated in the model avoiding to delete states of S to achieve that reduction. Through the equivalence relationship, we build the global profile for all the EBV in NPC sequences, this model allows us to represent the underlying and common stochastic law of the set of sequences. The equivalence classes define an optimal partition of {1, 2,…, p} × S, and it is in relation to this partition that we define the profile of the set of genomic sequences.

In this paper we investigate the consistency of quality indicators of the Brazilian public educational system. According to the newspaper Estado de São Paulo – Brazil, of January 18, 2017, only 7.3% of students in the third year of high school have an adequate level of mathematics, this shows the relevance of the evaluation and assessment of the Brazilian educational system. In this paper we explore the dependence between two indicators: (i) mean value between the proportions (in two subjects: Portuguese and Mathematics) of students under the basic level (SARESP classification) and (ii) rate of fails, during the years 2013, 2014 and 2015. (i) and (ii) are bases to define the educational quality of public schools for the population of young people, between 14 and 17 years old. This inspection is carried out through the Bayesian estimation of the parameters of the Asymmetric Cubic Sections (ACS) copula. We show that the dependence profile, year after year, behaves in a very unstable way, although during those years there were no substantial changes which justify such instability. Through the copula we compute conditional probabilities of tail events. We verify that an inversion occurred in the concordance/discordance between (i) and (ii). We compute the probability of (i) assuming high values, conditioned to a threshold in (ii). In 2013, as the threshold in (ii) increases the probability increases (concordance), in 2014 the threshold in (ii) is almost irrelevant to the probability and in 2015, as the threshold in (ii) increases the probability decreases (discordance). The inspection of the tail dependence allows to expose some kind of manipulation, in view of for instance, the maintenance of a global index índice de desenvolvimento da educação de São Paulo (IDESP) used to classify the educational institutions.

In this paper, we estimate tail conditional probabilities by incorporating copula models and adopting a Bayesian estimation process for the copula’s parameter. Based on the records of student’s classifications in (a) Mathematics and (b) Natural Sciences/Physics (of the entrance exam to the University of Campinas, from 2013 to 2015), by means of tail conditional probabilities we predict the performance, of the same students, in Calculus I which is a mandatory subject of the undergraduate course of Statistics, and we compare the conditional probabilities year after year. We see that (a), (b) and Calculus I show maximal trivariate correlations in tail events given by classifications which are jointly high/low in the three subjects. We compare the evolution of the tail conditional probabilities from 2013 to 2015 and, according to our results there has been an improvement (from 2013 to 2015) of at most 12%. This improvement being more incisive in the settings with conditional events given by jointly high classifications in comparison with settings with conditional events given by jointly lower classifications.

In this paper, we classify by representativeness the elements of a set of complete genomic sequences of Dengue Virus Type 1 (DENV-1), corresponding to the outbreak in Japan during 2014. The set is coming from four regions: Chiba, Hyogo, Shizuoka and Tokyo. We consider this set as composed of independent samples coming from Markovian processes of finite order and finite alphabet. Under the assumption of the existence of a law that prevails in at least 50% of the samples of the set, we identify the sequences governed by the predominant law (see [1, 2]). The rule of classification is based on a local metric between samples, which tends to zero when we compare sequences of identical law and tends to infinity when comparing sequences with different laws. We found that the order of representativeness, from highest to lowest and according to the origin of the sequences is: Tokyo, Chiba, Hyogo, and Shizuoka. When comparing the Japanese sequences with their contemporaries from Asia, we find that the less representative sequence (from Shizuoka) is positioned in groups considerably far away from that which includes the sequences from the other regions in Japan, this offers evidence to suppose that the outbreak in Japan could be produced by more than one type of DENV-1.