Hea-Jung Kim

Mn-implanted dilute magnetic semiconductor InP:Mn

Unintentionally doped bulk InP was prepared by the liquid encapsulated Czochralski method and subsequently implanted with various doses of Mn+. The properties of Mn+-implanted InP:Mn were investigated by various measurements. The results of energy dispersive x-ray peaks displayed injected concentrations of Mn of 0.8% and 8.8%, respectively. The results of photoluminescence (PL) measurement showed that optical broad transitions related to Mn appeared near 1.089, 1.144, and 1.185 eV in samples with various doses of Mn+. It was confirmed that the photoluminescence peaks near 1.089, 1.144, and 1.185 eV were Mn-correlated PL bands by the implantation of Mn. Ferromagnetic hysteresis loops measured at 10 K were observed and the temperature-dependent magnetization showed ferromagnetic behavior around 90 K, which almost agreed with the theoretical prediction (Tc∼70u2009K).

On a class of two-piece skew-normal distributions

In this article, a class of uni/bimodal distributions is proposed as a model for data concentrated about two directions in roughly equal proportions. This is an extension of earlier work on the skew-normal distribution introduced by Azzalini [Azzalini, A., 1985, A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171–178.]. The class, which depends on a shape parameter θu2009∈u2009(−∞, ∞), includes the normal distribution as a special case. Further, it defines yet another conditional distribution of compositely truncated bivariate normal distributions. Some distributional properties and inferences of the class are studied and further extensions are described. A sample of 850 KEBIX (Korea e-business index) scores is shown to be well described by this model.

BINARY REGRESSION WITH A CLASS OF SKEWED t LINK MODELS

ABSTRACT In this paper we propose a class of skewed t link models for analyzing binary response data with covariates. It is a class of asymmetric link models designed to improve the overall fit when commonly used symmetric links, such as the logit and probit links, do not provide the best fit available for a given binary response dataset. Introducing a skewed t distribution for the underlying latent variable, we develop the class of models. For the analysis of the models, a Bayesian and non-Bayesian methods are pursued using a Markov chain Monte Carlo (MCMC) sampling based approach. Necessary theories involved in modelling and computation are provided. Finally, a simulation study and a real data example are used to illustrate the proposed methodology.

A class of rectangle-screened multivariate normal distributions and its applications

A screening problem is tackled by proposing a parametric class of distributions designed to match the behavior of the partially observed screened data. This class is obtained from the nontruncated marginal of the rectangle-truncated multivariate normal distributions. Motivations for the screened distribution as well as some of the basic properties, such as its characteristic function, are presented. These allow us a detailed exploration of other important properties that include closure property in linear transformation, in marginal and conditional operations, and in a mixture operation as well as the first two moments and some sampling distributions. Various applications of these results to the statistical modelling and data analysis are also provided.

On the Ratio of Two Folded Normal Distributions

A class of distributions associated with the ratio of two folded normal random variables is introduced which strictly includes the half standard Cauchy distribution. The properties of this class of distributions are studied, along with a graph of the possible shapes of its density functions. The salient features of this class are mathematical tractability and statistical applicability. Utility of the class of distributions is demonstrated by presenting four applications.

A hierarchical Bayesian regression model for the uncertain functional constraint using screened scale mixtures of Gaussian distributions

This paper considers a hierarchical Bayesian analysis of regression models using a class of Gaussian scale mixtures. This class provides a robust alternative to the common use of the Gaussian distribution as a prior distribution in particular for estimating the regression function subject to uncertainty about the constraint. For this purpose, we use a family of rectangular screened multivariate scale mixtures of Gaussian distribution as a prior for the regression function, which is flexible enough to reflect the degrees of uncertainty about the functional constraint. Specifically, we propose a hierarchical Bayesian regression model for the constrained regression function with uncertainty on the basis of three stages of a prior hierarchy with Gaussian scale mixtures, referred to as a hierarchical screened scale mixture of Gaussian regression models (HSMGRM). We describe distributional properties of HSMGRM and an efficient Markov chain Monte Carlo algorithm for posterior inference, and apply the proposed model to real applications with constrained regression models subject to uncertainty.

Classification of a screened data into one of two normal populations perturbed by a screening scheme

In normal classification analysis, there may be cases where the population distributions are perturbed by a screening scheme. This paper considers a new classification method for screened data that is obtained from the perturbed normal distributions. Properties of each population distribution is considered and the best region for classifying the screened data is obtained. These developments yield yet another optimal rule for the classification. The rule is studied from several aspects such as a linear approximation, error rates, and estimation of the rule using the EM algorithm. Relationships among these aspects as well as investigation of the rules performance are also considered. The screened classification ideas are illustrated in detail using numerical examples.

Classification of Observations into One of Two Artificially Dichotomized Classes by Using a Normal Screening Variable

This article considers a problem of normal based two group classification when the groups are artificially dichotomized by a screening variable. Each group distribution is derived and the best regions for the classification are obtained. These derivations yield yet another classification rule. The rule is studied from several aspects such as the distribution of the rule, the optimal error rate, and the testing of a hypothesis. This article gives relationships among these aspects along with the investigation of the performance of the rule. The classification method and ideas are illustrated in detail with two examples.

A class of weighted normal distributions and its variants useful for inequality constrained analysis

This article develops a class of the weighted normal distributions for which the probability density function has the form of a product of a normal density and a weight function. The class constitutes marginal distributions obtained from various kinds of doubly truncated bivariate normal distributions. This class of distributions strictly includes the normal, skew–normal and two-piece skew–normal and is useful for selection modelling and inequality constrained normal mean analysis. Some distributional properties and Bayesian perspectives of the class are given. Probabilistic representation of the distributions is also given. The representation is shown to be straightforward to specify distribution and to implement computation, with output readily adapted for required analysis. Necessary theories and illustrative examples are provided.

A monte carlo method for estimating prediction limit for the arithmetic mean of lognormal sample

A Monte Carlo (MC) method is suggested for calculating an upper prediction limit for the mean of a future sample of small size N from a lognormal distribution. This is done by obtaining a Monte Carlo estimator of the limit utilizing the future sample generated from the Gibbs sampler. For the Gibbs sampler, a full conditional posterior predictive distribution of each observation in the future sample is derived. The MC method is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries. In an example, practical application of the method is described.