Application of Esscher Transformed Laplace Distribution in Microarray Gene Expression Data

Abstract

Microarrays allow the study of the expression profile of hundreds to thousands of genes simultaneously. These expressions could be from treated samples and the healthy controls. The Esscher transformed Laplace distribution is used to fit microarray expression data as compared to Normal and Laplace distributions. The Maximum Likelihood Estimation procedure is used to estimate the parameters of the distribution. R codes are developed to implement the estimation procedure. A simulation study is carried out to test the performance of the algorithm. AIC and BIC criterion are used to compare the distributions. It is shown that the fit of the Esscher transformed Laplace distribution is better as compared to Normal and standard Laplace distributions.

Transmuted esscher transformed laplace distribution and its application to microarray analysis

“…A smaller value of AIC and BIC indicates a better fit, and hence, T ET L fit the data better than ET L or Gaussian distributions. Devika et al (2016) used Esscher transformed Laplace distribution in modeling microarray data as an alternative to normal and Laplace distribution. In this work, we have proposed a new statistical model for the distribution of differential gene expression, which is a heavy tailed generalization of Laplace distribution.…”

“…After normalization, gene expression distribution (log ratio of red and green intensity measurements) which is referred to as error distribution has heavier tails than Gaussian distribution and has asymmetry of varying degrees. The error distribution is modeled using several densities, Devika et al (2016) used Esscher transformed Laplace distribution in modeling microarray data as an alternative to normal and Laplace distribution. Various authors suggested error distribution for gene expression data, asymmetric Laplace distribution (Purdom and Holmes, 2005), asymmetric type II compound Laplace , slash distribution with normal kernel (Punathumparambath, 2011), asymmetric slash Laplace (Punathumparambath, 2012a), skew slash t (Punathumparambath, 2012b), Laplace mixture (Punathumparambath and Kannan, 2012), slash distribution with Cauchy kernel (Punathumparambath, 2013), Double Lomax (Punathumparambath and Kulathinal, 2015) and compound exponential power (Punathumparambath, 2020).…”