In this article, we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatiotemporal dependence. Specifically, we propose to consider stochastic processes obtained through a monotone transformation of scaled version of χ² random processes. The latter is well known in the specialized literature and originates by summing independent copies of a squared Gaussian process. However, their use as stochastic models and related inference has not been much considered. Motivated by a spatiotemporal analysis of wind speed data from a network of meteorological stations in the Netherlands, we exemplify our modeling strategy by means of a nonstationary process with Weibull marginal distributions. For the proposed Weibull process we study the second‐order and geometrical properties and we provide analytic expressions for the bivariate distribution. Since the likelihood is intractable, even for a relatively small data set, we suggest adopting the pairwise likelihood as a tool for inference. Moreover, we tackle the prediction problem and we propose to use a linear prediction. The effectiveness of our modeling strategy is illustrated by analyzing the aforementioned Netherland wind speed data that we integrate with a simulation study. The proposed method is implemented in the R package GeoModels.

Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and mathematical tractability. However, this assumption seems to be restrictive when dealing with counting data. To deal with this situation, we propose a random field with a Poisson marginal distribution considering a sequence of independent copies of a random field with an exponential marginal distribution as “inter-arrival times” in the counting renewal processes framework. Our proposal can be viewed as a spatial generalization of the Poisson counting process. Unlike the classical hierarchical Poisson Log-Gaussian model, our proposal generates a (non)-stationary random field that is mean square continuous and with Poisson marginal distributions. For the proposed Poisson spatial random field, analytic expressions for the covariance function and the bivariate distribution are provided. In an extensive simulation study, we investigate the weighted pairwise likelihood as a method for estimating the Poisson random field parameters. Finally, the effectiveness of our methodology is illustrated by an analysis of reindeer pellet-group survey data, where a zero-inflated version of the proposed model is compared with zero-inflated Poisson Log-Gaussian and Poisson Gaussian copula models. Supplementary materials for this article, including technical proofs and R code for reproducing the work, are available as an online supplement.

In this paper, we develop two fully parametric quantile regression models, based on the power Johnson $S_B$ distribution for modeling unit interval response in different quantiles. In particular, the conditional distribution is modeled by the power Johnson $S_B$ distribution. The maximum likelihood (ML) estimation method is employed to estimate the model parameters. Simulation studies are conducted to evaluate the performance of the ML estimators in finite samples. Furthermore, we discuss influence diagnostic tools and residuals. The effectiveness of our proposals is illustrated with a data set of the mortality rate of COVID-19 in different countries. The results of our models with this data set show the potential of using the new methodology. Thus, we conclude that the results are favorable to the use of proposed quantile regression models for fitting double bounded data.