Estimation Of Distribution Type And Parameters Based On Multimodal Histograms

In many applications involving measuring a physical phenomenon, the output data contains a mixture of different type of distributions. The data set consists often of unimodal distributions, which overlap, i.e. the ranges of the corresponding random variables have a significant intersection. After observing a multimodal histogram that has several partially overlapping distributions the aim is to separate them by inferring the correct types of the probability density functions (PDFs) and their parameters. The method is based on the non-linear least squares estimation, where several types of PDFs are fitted to the region mostly affected by a single distribution. The possible candidate PDFs are those of the Pearson system, Weibull, Fisher, chi-squared and Rayleigh distributions. This method can be extended to multidimensional cases in certain situations. The methods developed earlier for this task are based for example on the QQ-plot technique and on order statistic filter banks. The found distribution types and their parameters can be applied to different tasks in image processing and system analysis. This algorithm can be used e.g. to the estimation of PDFs of certain phenomena and to global thresholding of images. The method is applied to real two-dimensional data sets having values coming from several distributions.