A random variable is difference-form decomposable (DFD) if it may be written as the difference of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifically, a DFD density can be neither approximately uniform, nor quasi convex, nor...

We develop a distribution regression model under endogenous sample selection. This model is a semi-parametric generalization of the Heckman selection model. It accommodates much richer effects of the covariates on outcome distribution and patterns of heterogeneity in the selection process, and...

The bacterial synthesis of copper nanoparticles (CuNPs) emerges as an eco-friendly alternative to conventional techniques since it comprises a single-step and bottom-up approach, which leads to stable metal nanoparticles. In this paper, we studied the biosynthesis of Cu-based nanoparticles by...

Multivariate distributional forecasts have become widespread in recent years. To assess the quality of such forecasts, suitable evaluation methods are needed. In the univariate case, calibration tests based on the probability integral transform (PIT) are routinely used. However, multivariate...

We characterize the distributions of posterior quantiles under a given prior. Unlike the distributions of posterior means, which are known to be mean-preserving contractions of the prior, the distributions of a posterior quantile coincide with a first-order stochastic dominance interval bounded...

When datasets present long conditional tails on their response variables, algorithms based on Quantile Regression have been widely used to assess extreme quantile behaviors. Value at Risk (VaR) and Conditional Tail Expectation (CTE) allow the evaluation of extreme events to be easily...

In this study, we deal with the hypothesis testing problem of Poisson distributed data. The purpose of the test is to determine whether two collections of discrete data have the same Poisson rate. We review and compare several frequientist and Bayesian methods that deal with the problem, such as...

In density forecasts, respondents are asked to assign probabilities to pre-specified ranges of inflation. We show in two large-scale experiments that responses vary when we modify the response scale. Asking an identical question with modified response scales induces different answers: Shifting,...

This paper derives a new decomposition of stock returns using price extremes and proposes a conditional autoregressive shape (CARS) model with beta density to predict the direction of stock returns. The CARS model is continuously valued, which makes it different from binary classification...