Springer Science and Business Media LLC

In this article, we propose a generalization to the Gaussian process regression(GPR) model called the extended skew Gaussian process for regression (ESGP) model. The ESGP model works better than the GPR model when the errors are skewed. We derive the predictive distribution for the ESGP model at a new input. Also we apply the ESGP model to FOREX data and we find that it fits the Forex data better than the GPR model.

Power-expected-posterior (PEP) priors have been recently introduced as generalized versions of the expected-posterior-priors (EPPs) for variable selection in Gaussian linear models. They are minimally-informative priors that reduce the effect of training samples under the EPP approach, by combining ideas from the power-prior and unit-information-prior methodologies. In this paper we prove the information consistency of the PEP methodology, when using the independence Jeffreys as a baseline prior, for the variable selection problem in normal linear models.

We present two seminal contributions of Corrado Gini on the theory of survey sampling and the theory of inequalities: the idea of balanced sampling and the Gini inequality index. These contributions have contributed to the development of a fertile field of research.

The expected-posterior prior (EPP) and the power-expected-posterior (PEP) prior are based on random imaginary observations and offer several advantages in objective Bayesian hypothesis testing. The use of sufficient statistics, when these exist, as a way to redefine the EPP and PEP prior is investigated. In this way the dimensionality of the problem can be reduced, by generating samples of sufficient statistics instead of generating full sets of imaginary data. On the theoretical side it is proved that the new EPP and PEP definitions based on imaginary training samples of sufficient statistics are equivalent with the standard definitions based on individual training samples. This equivalence provides a strong justification and generalization of the definition of both EPP and PEP prior, since from the individual samples or from the sufficient samples the criteria coincide. This avoids potential inconsistencies or paradoxes when only sufficient statistics are available. The applicability of the new definitions in different hypotheses testing problems is explored, including the case of an irregular model. Calculations are simplified; and it is shown that when testing the mean of a normal distribution the EPP and PEP prior can be expressed as a beta mixture of normal priors. The paper concludes with a discussion about the interpretation and the benefits of the proposed approach.

The random variable X t = X − t¦X ≥ t, which is called the residual life random variable, has gathered the attention of most researchers in reliability. The mean and the variance of this variable in continuous distribution have been studied by several authors. But, in discrete case, only in recent years, some studies have been done for the mean of this variable. In this paper, we define and study the properties of variance of T k = T − k¦T ≥ k where T is a discrete random variable. Besides similar results for discrete and continuous lifetime distributions, relationships with its mean, monotonicity and the associated ageing classes of distributions are obtained for discrete cases. Furthermore, some characterization results about the class of increasing (decreasing) variance residual life distributions based on mean residual life and residual coefficient of variation, are presented and the lower and upper bound for them are achieved.