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

Leiva, Víctor; Sanhueza, Antonio; Kelmansky, Diana; Martı́nez, Elena

doi:10.1016/j.csda.2008.04.012

Cited by 10 publications

(7 citation statements)

References 6 publications

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“…This paper extends the results previously presented by Leiva and coauthors [ 11 ] and therefore the new distribution family offers a larger set of models. Considering the Leiva et al proposal as a standard alternative, the new family can fit data for which their proposal might be not flexible enough.…”

Section: Discussionsupporting

confidence: 85%

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A New Distribution Family for Microarray Data

Kelmansky

Ricci

2017

Microarrays

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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∈double-struckR 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.

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Section: Discussionsupporting

confidence: 85%

“…One advantage of this strategy is that it facilitates a direct interpretation of the results. In this direction, [ 11 ] showed that data that become normal after a glog transformation belong to what they called the glog -normal distribution family.…”

Section: Introductionmentioning

confidence: 99%

A New Distribution Family for Microarray Data

Kelmansky

Ricci

2017

Microarrays

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“…In addition, from (6), we note that a transformation known as the generalized logarithm (glog) is being used, which is defined as glog(z) = arcsinh(z) = log(z + √ z 2 +1); see [21].…”

Section: Remarkmentioning

confidence: 99%

“…In some cases, researchers transform the response to eliminate the skewness and hence applying procedures for normal regression. However, in spite of the common use of data transformations, it has been shown that analyses upon wrong transformations reduce the power of the study; see [21] and the references therein. In addition, even if an appropriate transformation of data is applied, interpretation problems are transferred to the parameters of the normal regression model.…”

Section: Introductionmentioning

confidence: 99%

Robust statistical modeling using the Birnbaum‐Saunders‐t distribution applied to insurance

Paula

Leiva

Barros

et al. 2011

Appl Stoch Models Bus & Ind

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In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model.

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“…However, it has been shown that analyses performed under an inappropriate data transformation reduce the power of the study; see Huang and Qu [12], Leiva et al [18] and references therein. In any case, even when an appropriate transformation is used, a problem of data interpretation still remains.…”

Section: Introductionmentioning

confidence: 98%