This article addresses various properties and estimation methods for the Exponentiated Chen distribution. Although, our main focus is on estimation from frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures, namely, the method of maximum likelihood estimation, percentile estimation, least square and weighted least-square estimation, maximum product of spacings estimation, Cramér-von-Mises estimation, Anderson–Darling, and right-tail Anderson–Darling estimation. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of three real datasets.

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.

In this study, we present different estimation procedures for the parameters of the Poisson–exponential distribution, such as the maximum likelihood, method of moments, modified moments, ordinary and weighted least-squares, percentile, maximum product of spacings, Cramer–von Mises and the Anderson–Darling maximum goodness-of-fit estimators and compare them using extensive numerical simulations. We showed that the Anderson–Darling estimator is the most efficient for estimating the parameters of the proposed distribution. Our proposed methodology was also illustrated in three real data sets related to the minimum, average and the maximum flows during October at São Carlos River in Brazil demonstrating that the PE distribution is a simple alternative to be used in hydrological applications.

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.