Valmária Rocha da Silva ∗ Fernando Antônio da Silva Moura † Abstract The main aim of this work is to propose two important connected extensions of the Fay and Heriot (1979) area level small area estimation model that might be of practical and theoretical interests. The first extension allows for the sampling error to be non-symmetrically distributed. This is important for the case that the samp...

One problem of skew normal model is the difficulty in estimating the shape parameter, for which the maximum likelihood estimate may be infinite when sample size is moderate. The existing estimators suffer from large bias even for moderate size samples. In this paper, we proposed five estimators of the shape parameter for a scalar skew normal model, either by bias correction method or by solving...

• Modeling real data sets, even when we have some potential (as)symmetric models for the underlying data distribution, is always a very difficult task due to some uncontrollable perturbation factors. The analysis of different data sets from diverse areas of application, and in particular from statistical process control (SPC), leads us to notice that they usually exhibit moderate to strong asym...

Skewness is often present in a wide range of applied problems. One possible approach to model this skewness is based on the class of skew normal distributions. Fitting such distributions remains an inference challenge in various cases. In this paper, we propose and study novel estimators using weighted moments for the closed multivariate skew-normal distribution.

For solving large sparse non-Hermitian positive definite linear equations, Bai et al. proposed the Hermitian and skew-Hermitian splitting methods (HSS). They recently generalized this technique to the normal and skew-Hermitian splitting methods (NSS). In this paper, we present an accelerated normal and skew-Hermitian splitting methods (ANSS) which involve two parameters for the NSS iteration. W...

The mod 2 normality of a real number is defined with respect to measurable subsets in the unit interval and the coboundary condition is obtained. The relation with skew product transformation is also investigated. 1991 Mathematics Subject Classification. Primary 28D05, 58F11, 11K16.

Classes of shape mixtures of independent and dependent multivariate skew-normal distributions are considered and some of their main properties are studied. If interpreted from a Bayesian point of view, the results obtained in this paper bring tractability to the problem of inference for the shape parameter, that is, the posterior distribution can be written in analytic form. Robust inference fo...

The entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions. We study...

Asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied. The asymptotic normality of the pseudo-maximum likelihood estimator is derived using the two-step estimation procedure. The t distribution assumption and the skew-normal distribution assumption are used as alternatives to the normal distribution assumption in a num...

Several papers on distributions to model rates and proportions have been recently published; their fitting in numerous instances is better than the alternative beta distribution, which has distribution follow when it necessary quantify average of a response variable based set covariates. Despite great usefulness this fit responses (0,1) unit interval, its relevance loses objectivity interest qu...