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

The Original Article was published on 13 January 2004

## 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/{(2Ï€)1/2 Ïƒ(r i - Î³)}] exp [-{log(r i - Î³) - Î¼}2/2Ïƒ2] for r i > Î³,

where k is a compensation constant (k = loge = 0.4343), Ïƒ and Î¼ are the shape and scale parameters for log(r i - Î³), respectively.

The threshold parameter, Î³, was found through trial and improvement calculation processes; in the trial, the distribution of log(r i - Î³) was checked by normal probability plotting, and the value that gave the best fit to the model was selected for Î³. The fitness was evaluated by the sum of absolute differences between the model and log(r i - Î³), within the interquartile range of data. The parameter Î¼ was found as the median of log(r i - Î³), and the parameter Ïƒ was found from the interquartile range of log(r i - Î³); these are known as robust alternatives for the arithmetic mean and standard deviation, respectively. Parameters Î¼ and Ïƒ 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 - Î³) - Î¼}/Ïƒ.

Intensity data (r i ) less than Î³ were treated as "data not detected", since such data might contain negative noise larger than the signal (see Results).

## 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. 10.1186/1471-2105-5-5

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Correspondence to Tomokazu Konishi.

The online version of the original article can be found at 10.1186/1471-2105-5-5

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