Using logarithmically binned data greatly accelerates the fitting procedure and introduces significant errors only for bins spaced more widely than 8-16 per decade.
Logarithmic binning with a square root transformation simplifies the interpretation and manual fitting of single-channel dwell time distributions containing multiple exponential components.
A.L. Blatz and K.L. Magleby (1986a. J. Physiol. Lond.. 378:141-174) have demonstrated the usefulness of plotting histograms with a logarithmic time axis to display the distributions of dwell times from recordings of single ionic channels. We derive here the probability density function (pdf) corresponding to logarithmically binned histograms. Plotted on a logarithmic time scale the pdf is a peaked function with an invariant width; this and other properties of the pdf, coupled with a variance-stabilizing (square root) transformation for the ordinate, greatly simplify the interpretation and manual fitting of distributions containing multiple exponential components. We have also examined the statistical errors in estimation, by the maximum-likelihood method, of kinetic parameters from logarithmically binned data. Using binned data greatly accelerates the fitting procedure and introduces significant errors only for bins spaced more widely than 8-16 per decade.
Sigworth et al. (1987) studied this question. Logarithmic binning and variance-stabilizing transformation was evaluated on Statistical errors in estimation of kinetic parameters. Using logarithmically binned data greatly accelerates the fitting procedure and introduces significant errors only for bins spaced more widely than 8-16 per decade.