center dot The family of Unified Skew Normal distributions is associated with probability distributions encountered in various problems, notably those of the selection of individuals in a normal population. In this work, we focus on the ordering of the real subfamily of this class of distributions with respect to its parameters and for some stochastic orders (usual order, increasing convex order, increasing concave order and likelihood ratio order). Our results are applied to a reliability problem as well as a selection problem.
In this paper, we present a Bayesian variable selection method for zero-inflated longitudinal data. For this purpose, we consider a zero-inflated power series random effects model that includes the zero-inflated Poisson and negative binomial random effects models. We propose using continuous spike and Dirac spike priors to simultaneously estimate the regression coefficients and select the important covariate variables. We apply the MCMC method using Gibbs sampling for posterior inference. Some simulation studies are performed to investigate the performance of the proposed approach, and it is also applied to analyze a real dataset from the RAND Health Insurance Experiment.
center dot Misuse of statistical significance continues to be prevalent in science. The absence of intuitive explanations of this concept often leads researchers to incorrect conclusions. For this reason, some statisticians suggest adopting S-values (surprisals) instead of P-values, as they relate the statistical relevance of an event to the number of consecutive heads when flipping an unbiased coin. This paper introduces the concept of surprisal intervals (S-intervals) as extensions of confidence/compatibility intervals. The proposed approach imposes the assessment of outcomes in terms of more and less surprising than some values, instead of statistically significant and statistically non-significant. Moreover, a novel methodology for presenting multiple consecutive S-intervals (or compatibility intervals as well) in order to evaluate the variation in surprise (or compatibility) with various target hypotheses is discussed.
This paper is the next step ahead in constructing probability distribution of changeable flatness of PDF that is expressed with well-known kurtosis measure. The distribution in question is named the Extended Easily Changeable Kurtosis and descends from the Easily Changeable Kurtosis. The paper covers PDF, CDF, modes and inflection points, quantiles, moments and Moors' measure and the Fisher Information Matrix. In addition generator of pseudo-random numbers that follow the Extended Easily Changeable Kurtosis is presented. Unknown parameters of the distribution are estimated with the maximum likelihood method. The paper ends with illustrative examples of applicability and flexibility of the new distribution. The most important R codes are presented in the supplementary material.
center dot Model specification and selection are important aspects of modeling exercises. In this context, the Fisher Information Matrix (FIM) plays an essential role. In this paper, we derive the Fisher Information Matrix (FIM) for the two way random effects panel data models in general as well as in some specific cases of heteroscedasticity. Some computational issues are then raised and discussed. In addition, some real data examples are reported and thoroughly discussed.
