On the glog-normal distribution and its application to the gene expression problem

A New Distribution Family for Microarray Data

The traditional approach with microarray data has been to apply transformations that approximately normalize them, with the drawback of losing the original scale. The alternative standpoint taken here is to search for models that fit the data, characterized by the presence of negative values, preserving their scale; one advantage of this strategy is that it facilitates a direct interpretation of the results. A new family of distributions named gpower-normal indexed by p∈R is introduced and it is proven that these variables become normal or truncated normal when a suitable gpower transformation is applied. Expressions are given for moments and quantiles, in terms of the truncated normal density. This new family can be used to model asymmetric data that include non-positive values, as required for microarray analysis. Moreover, it has been proven that the gpower-normal family is a special case of pseudo-dispersion models, inheriting all the good properties of these models, such as asymptotic normality for small variances. A combined maximum likelihood method is proposed to estimate the model parameters, and it is applied to microarray and contamination data. R codes are available from the authors upon request.

Air contaminant statistical distributions with application to PM10 in Santiago, Chile

The use of statistical distributions to predict air quality is valuable for determining the impact of air chemical contaminants on human health. Concentrations of air pollutants are treated as random variables that can be modeled by a statistical distribution that is positively skewed and starts from zero. The type of distribution selected for analyzing air pollution data and its associated parameters depend on factors such as emission source and local meteorology and topography. International environmental guideline use appropriate distributions to compute exceedance probabilities and percentiles for setting administrative targets and issuing environmental alerts. The distribution bears a relationship to the normal distribution, and there are theoretical - and physical-based mechanistic arguments that support its use when analyzing air-pollutant data. Others distribution have also been used to model air population data, such as the beta, exponential, gamma, Johnson, log-logistic, Pearson, and Weibull distribution. One model also developed from physical-mechanistic considerations that has received considerable interest in recent year is the Birnbaum-Saunders distribution. This distribution has theoretical arguments and properties similar to those of the log-normal distribution, which renders it useful for modeling air contamination data. In this review, we have addressed the range of common atmospheric contaminants and the health effects they cause. We have also reviewed the statistical distributions that have been use to model air quality, after which we have detailed the problem of air contamination in Santiago, Chile. We have illustrated a methodology that is based on the Birnbaum-Saunders distributions to analyze air contamination data from Santiago, Chile. Finally, in the conclusions, we have provided a list of synoptic statements designed to help readers understand the significance of air pollution in Chile, and in Santiago, in particular, but that can be useful to other cites and countries.