On probability distribution functions in turbulence. Part 1. A regularisation method to improve the estimate of a PDF from an experimental histogram

The most common method to estimate a probability distribution function (PDF) from experimental data is to compute a normalised histogram. This approximation implicitly assumes that the PDF is smooth at the scale of one histogram bin. Usually, the normalised histogram is ill defined for the rarer events since the points are very scattered in that region. In order to increase the quality of the PDF estimate, the assumption that the PDF is smooth can be used explicitly. A specially designed regularisation method is constructed and tested on both synthetic and real turbulence signals. Using this procedure, the estimated PDFs are now smooth and well-defined up to the unique rarest event (the last histogram point). Among its direct applications, the method allows to get a better estimate of high order PDF moments and of PDFs convolution products. (C) 1999 Elsevier Science B.V. All rights reserved.