Open Access

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

BMC Bioinformatics20045:82

DOI: 10.1186/1471-2105-5-82

Received: 28 June 2004

Accepted: 28 June 2004

Published: 28 June 2004

The original article was published in BMC Bioinformatics 2004 5:5

Correction to formulae in methods section [1]

The lognormal distribution model and estimation of the parameters

The method assumes that the original intensity data, (r i ) for i = 1,2...n, obey a lognormal distribution. The probability density function of the intensity data used was:

f(r i ) = [k/{(2π)1/2 σ(r i - γ)}] exp [-{log(r i - γ) - μ}2/2σ2] for r i > γ,

where k is a compensation constant (k = loge = 0.4343), σ and μ are the shape and scale parameters for log(r i - γ), respectively.

The threshold parameter, γ, was found through trial and improvement calculation processes; in the trial, the distribution of log(r i - γ) was checked by normal probability plotting, and the value that gave the best fit to the model was selected for γ. The fitness was evaluated by the sum of absolute differences between the model and log(r i - γ), within the interquartile range of data. The parameter μ was found as the median of log(r i - γ), and the parameter σ was found from the interquartile range of log(r i - γ); these are known as robust alternatives for the arithmetic mean and standard deviation, respectively. Parameters μ and σ were found for each data grid, a group of data for DNA spots that were printed by an identical pin in order to avoid divergences caused by pin-based differences. Z-normalization was carried out for each datum as

Z ri = {log(r i - γ) - μ}/σ.

Intensity data (r i ) less than γ were treated as "data not detected", since such data might contain negative noise larger than the signal (see Results).

Notes

Authors’ Affiliations

(1)
Faculty of Bioresource Sciences, Akita Prefectural University

References

  1. Tomokazu Konishi : Three-parameter lognormal distribution ubiquitously found in cDNA microarray data and its application to parametric data treatment. BMC Bioinformatics 2004, 5: 5. 10.1186/1471-2105-5-5PubMed CentralView ArticlePubMedGoogle Scholar

Copyright

© Konishi; licensee BioMed Central Ltd. 2004

This article is published under license to BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL.

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