In the paper, the inverse Nakagami-m (NK) distribution is proposed. This distribution is the reciprocal of the NK model that plays an important role in the general area of the communications engineering and reliability system. The proposed model is useful to describe devices that are subjected to high stress, providing high failure rate after a short repair time. An account of mathematical properties is presented such as the rth moment, mean, variance, rth central moment, survival properties, and Shannon’s entropy. The maximum-likelihood estimators are explored under complete and censored data, but a bias correction was applied to the order $O(n^{-2})$ for obtaining nearly unbiased performance. An efficient closed-form maximum a posteriori (MAP) estimator was also proposed. A simulation study compares the performance of the estimators with a clear advantage for the closed-form MAP one. Finally, we illustrate the new distribution fitting on three real datasets.

Spatial documentation is exponentially increasing given the availability of Big Data in the Internet of Things, enabled by device miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence structure and hidden patterns in space through prior knowledge and data likelihood. However, this class of modeling is not yet well explored when compared to adopting classification and regression in machine-learning models, in which the assumption of the spatiotemporal independence of the data is often made, that is an inexistent or very weak dependence. Thus, this systematic review aims to address the main models presented in the literature over the past 20 years, identifying the gaps and research opportunities. Elements such as random fields, spatial domains, prior specification, the covariance function, and numerical approximations are discussed. This work explores the two subclasses of spatial smoothing: global and local.

Statistical monitoring tools are well established in the literature, creating organizational cultures such as Six Sigma or Total Quality Management. Nevertheless, most of this literature is based on the normality assumption, e.g., based on the law of large numbers, and brings limitations towards truncated processes as open questions in this field. This work was motivated by the register of elements related to the water particles monitoring (relative humidity), an important source of moisture for the Copiapó watershed, and the Atacama region of Chile (the Atacama Desert), and presenting high asymmetry for rates and proportions data. This paper proposes a new control chart for interval data about rates and proportions (symbolic interval data) when they are not results of a Bernoulli process. The unit-Lindley distribution has many interesting properties, such as having only one parameter, from which we develop the unit-Lindley chart for both classical and symbolic data. The performance of the proposed control chart is analyzed using the average run length (ARL), median run length (MRL), and standard deviation of the run length (SDRL) metrics calculated through an extensive Monte Carlo simulation study. Results from the real data applications reveal the tool’s potential to be adopted to estimate the control limits in a Statistical Process Control (SPC) framework.

Background: Using conventional tDCS over the temporo-parietal junction (TPJ) we previously reported that it is possible to manipulate subjective visual vertical (SVV) and postural control. We also demonstrated that high-definition tDCS (HD-tDCS) can achieve substantially greater cortical stimulation focality than conventional tDCS. However, it is critical to establish dose-response effects using well-defined protocols with relevance to clinically meaningful applications. Objective: To conduct three pilot studies investigating polarity and intensity-dependent effects of HD-tDCS over the right TPJ on behavioral and physiological outcome measures in healthy subjects. We additionally aimed to establish the feasibility, safety, and tolerability of this stimulation protocol. Methods: We designed three separate randomized, double-blind, crossover phase I clinical trials in different cohorts of healthy adults using the same stimulation protocol. The primary outcome measure for trial 1 was SVV; trial 2, weight-bearing asymmetry (WBA); and trial 3, electroencephalography power spectral density (EEG-PSD). The HD-tDCS montage comprised a single central, and 3 surround electrodes (HD-tDCS3x1) over the right TPJ. For each study, we tested 3x2 min HD-tDCS3x1 at 1, 2 and 3 mA; with anode center, cathode center, or sham stimulation, in random order across days. Results: We found significant SVV deviation relative to baseline, specific to the cathode center condition, with consistent direction and increasing with stimulation intensity. We further showed significant WBA with direction governed by stimulation polarity (cathode center, left asymmetry; anode center, right asymmetry). EEG-PSD in the gamma band was significantly increased at 3 mA under the cathode. Conclusions: The present series of studies provide converging evidence for focal neuromodulation that can modify physiology and have behavioral consequences with clinical potential.

We considered five generalizations of the standard Weibull distribution to describe the lifetime of two important components of sugarcane harvesting machines. The harvesters considered in the analysis harvest an average of 20 tons of sugarcane per hour and their malfunction may lead to major losses; therefore, an effective maintenance approach is of main interest for cost savings. For the considered distributions, mathematical background is presented. Maximum likelihood is used for parameter estimation. Further, different discrimination procedures were used to obtain the best fit for each component. At the end, we propose a maintenance scheduling for the components of the harvesters using predictive analysis.

In this paper, from the practical point of view, we focus on modeling traumatic brain injury data considering different stages of hospitalization, related to patients’ survival rates following traumatic brain injury caused by traffic accidents. From the statistical point of view, the primary objective is related to overcoming the limited number of traumatic brain injury patients available for studying by considering different estimation methods to obtain improved estimators of the model parameters, which can be recommended to be used in the presence of small samples. To have a general methodology, at least in principle, we consider the very flexible Generalized Gamma distribution. We compare various estimation methods using extensive numerical simulations. The results reveal that the penalized maximum likelihood estimators have the smallest mean square errors and biases, proving to be the most efficient method among the investigated ones, mainly to be used in the presence of small samples. The Simulated Annealing technique is used to avoid numerical problems during the optimization process, as well as the need for good initial values. Overall, we considered an amount of three real data sets related to traumatic brain injury caused by traffic accidents to demonstrate that the Generalized Gamma distribution is a simple alternative to be used in this type of applications for different occurrence rates and risks, and in the presence of small samples.