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Open Access Highly Accessed Methodology article

Three-parameter lognormal distribution ubiquitously found in cDNA microarray data and its application to parametric data treatment

Tomokazu Konishi

Author Affiliations

Faculty of Bioresource Sciences, Akita Prefectural University, Akita 010-0195, Japan

BMC Bioinformatics 2004, 5:5  doi:10.1186/1471-2105-5-5

Published: 13 January 2004



To cancel experimental variations, microarray data must be normalized prior to analysis. Where an appropriate model for statistical data distribution is available, a parametric method can normalize a group of data sets that have common distributions. Although such models have been proposed for microarray data, they have not always fit the distribution of real data and thus have been inappropriate for normalization. Consequently, microarray data in most cases have been normalized with non-parametric methods that adjust data in a pair-wise manner. However, data analysis and the integration of resultant knowledge among experiments have been difficult, since such normalization concepts lack a universal standard.


A three-parameter lognormal distribution model was tested on over 300 sets of microarray data. The model treats the hybridization background, which is difficult to identify from images of hybridization, as one of the parameters. A rigorous coincidence of the model to data sets was found, proving the model's appropriateness for microarray data. In fact, a closer fitting to Northern analysis was obtained. The model showed inconsistency only at very strong or weak data intensities. Measurement of z-scores as well as calculated ratios was reproducible only among data in the model-consistent intensity range; also, the ratios were independent of signal intensity at the corresponding range.


The model could provide a universal standard for data, simplifying data analysis and knowledge integration. It was deduced that the ranges of inconsistency were caused by experimental errors or additive noise in the data; therefore, excluding the data corresponding to those marginal ranges will prevent misleading analytical conclusions.