A competitive family to the Beta and Kumaraswamy generators: Properties, Regressions and Applications.

We define two new flexible families of continuous distributions to fit real data by compoun-ding the Marshall-Olkin class and the power series distribution. These families are very competitive to the popular beta and Kumaraswamy generators. Their densities have linear representations of exponentiated densities. In fact, as the main properties of thirty five exponentiated distributions are well-known, we can easily obtain several properties of about three hundred fifty distributions using the references of this article and five special cases of the power series distribution. We provide a package implemented in R software that shows numerically the precision of one of the linear representations. This package is useful to calculate numerical values for some statistical measurements of the generated distributions. We estimate the parameters by maximum likelihood. We define a regression based on one of the two families. The usefulness of a generated distribution and the associated regression is proved empirically.

The COVID-19 Pandemic in Brazil: Some Aspects and Tools.

The article presents some aspects related to the COVID-19 pandemic in Brazil including public health, challenges facing healthcare workers and adverse impacts on the country's economy. Its main contribution is the availability of two web applications for online monitoring of the evolution of the pandemic in Brazil and South America. The applications provide the possibility to download data in different formats, view interactive maps and graphs of the cumulative confirmed cases, deaths and lethality rates, in addition to presenting plots of moving averages for states and municipalities. The predictions about new cases and new deaths caused by COVID-19, in states and regions of Brazil, are also reported using GAMLSS models. The forecasts can be easily used by public managers for effective decision-making.

Covid-19 in Brazil: A sad scenario.

The main contribution of this article is to report general statistics about COVID-19 in Brazil, based on analysis of accumulated series of confirmed cases, deaths and lethality rates, in addition to presenting graphs of moving averages for states and municipalities. The data show that the pandemic in Brazil has grown rapidly since February 25th (date of the first reported case). Furthermore, the lethality rate of COVID-19 in Brazil is greater than in many other Latin American countries (Chile, Argentina, Uruguay and Paraguay). However, the number of new confirmed cases in Brazil has little statistical relevance because only a small part of the population has been tested. In relation to Brazilian municipalities, we highlight the 10 states with the highest lethality rates, ranked from highest to lowest. Also, predictions about the increaseor decrease innew cases and deaths for states and capital cities are presented. These results can help managers and researchers to better guide their decisions regarding COVID-19.

AdequacyModel: An R package for probability distributions and general purpose optimization.

Several lifetime distributions have played an important role to fit survival data. However, for some of these models, the computation of maximum likelihood estimators is quite difficult due to presence of flat regions in the search space, among other factors. Several well-known derivative-based optimization tools are unsuitable for obtaining such estimates. To circumvent this problem, we introduce the AdequacyModel computational library version 2.0.0 for the R statistical environment with two major contributions: a general optimization technique based on the Particle Swarm Optimization (PSO) method (with a minor modification of the original algorithm) and a set of statistical measures for assessment of the adequacy of the fitted model. This library is very useful for researchers in probability and statistics and has been cited in various papers in these areas. It serves as the basis for the Newdistns library (version 2.1) published in an impact journal in the area of computational statistics, see https://CRAN.R-project.org/package=Newdistns. It is also the basis of the Wrapped library (version 2.0), see https://CRAN.R-project.org/package=Wrapped. A third package making use of the AdequacyModel library can be found in https://CRAN.R-project.org/package=sglg. In addition, the proposed library has proved to be very useful for maximizing log-likelihood functions with complex search regions. The library provides a greater control of the optimization process by introducing a stop criterion based on a minimum number of iterations and the variance of a given proportion of optimal values. We emphasize that the new library can be used not only in statistics but in physics and mathematics as proved in several examples throughout the paper.