Identification algorithm for telecommunication systems with uncertain parameters of their vector of state stochastic model

The described method of structure identification of the state vector of a telecommunication system stochastic model is based on a posteriori probability density approximation (APDA) by a system of a posteriori moments. An assumption of possible APDA approximation by a class of Pearson distributions resulted in a closed system of moment equations. Implementation of optimal non-linear stochastic object control techniques helped to solve the problem of structural identification. Introduction of the proposed approach into contemporary telecommunication systems will not impose additional requirements on the calculating equipment, thus making this method well-suited for a wide range of applications.

Segmentation of Natural Images With K-Means and Hierarchical Algorithm Based on Mixture of Pearson Distributions

Image analysis and retrieval are most important for video processing, remote sensing, computer vision and security and surveillance. In an image, regional variation is more important for authentication and identification. Nowadays, the model based segmentation methods are more prominent and provide accurate results for segmentation of images. For ascribing a suitable model it is reasonable to consider the probability model, which closely matches with the physical features of the image region. In this paper a new and novel approach of image segmentation is carried using the Type III Pearsonian system of distributions. In the current work, it is considered that the entire picture is characterized by a K-component combination of Pearsonian Type III distribution. Using the EM algorithm, the performance parameters for the currently considered model are estimated. Through experimentation 4 real images randomly selected from the Berkeley image database. The computed values of PRI, GCE and VOI revealed that proposed method provide more accurate results to the same images in which the image regions are left skewed and having long upper tiles. Through image quality metrics the performance of image retrieval with the proposed method is also studied and found that this method outperforms then that of the segmentation method based on GMM. The results of the current model is being compared with the other existing previous models like the 3-paprameter regression models and the k-means hierarchical clustering models for various sets of input images and the results are displayed in the performance evaluation models chapter in detail.

Computing and graphing probability values of pearson distributions: a SAS/IML macro

Background Any empirical data can be approximated to one of Pearson distributions using the first four moments of the data (Elderton WP, Johnson NL. Systems of Frequency Curves. 1969; Pearson K. Philos Trans R Soc Lond Ser A. 186:343–414 1895; Solomon H, Stephens MA. J Am Stat Assoc. 73(361):153–60 1978). Thus, Pearson distributions made statistical analysis possible for data with unknown distributions. There are both extant, old-fashioned in-print tables (Pearson ES, Hartley HO. Biometrika Tables for Statisticians, vol. II. 1972) and contemporary computer programs (Amos DE, Daniel SL. Tables of percentage points of standardized pearson distributions. 1971; Bouver H, Bargmann RE. Tables of the standardized percentage points of the pearson system of curves in terms of β1 and β2. 1974; Bowman KO, Shenton LR. Biometrika. 66(1):147–51 1979; Davis CS, Stephens MA. Appl Stat. 32(3):322–7 1983; Pan W. J Stat Softw. 31(Code Snippet 2):1–6 2009) available for obtaining percentage points of Pearson distributions corresponding to certain pre-specified percentages (or probability values; e.g., 1.0%, 2.5%, 5.0%, etc.), but they are little useful in statistical analysis because we have to rely on unwieldy second difference interpolation to calculate a probability value of a Pearson distribution corresponding to a given percentage point, such as an observed test statistic in hypothesis testing. Results The present study develops a macro program to identify the appropriate type of Pearson distribution based on either input of dataset or the values of four moments and then compute and graph probability values of Pearson distributions for any given percentage points. Conclusions The SAS macro program returns accurate approximations to Pearson distributions and can efficiently facilitate researchers to conduct statistical analysis on data with unknown distributions.