Abstract
SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.
Abstract
The beta transformation gives a great variety of shapes which allow to model symmetric, skewed and bimodal shaped densities. Such procedure generates what we call the beta generalized (beta-G) family of distributions. This chapter presents a survey on the beta-G models and their mathematical properties. We present some explicit expressions for the ordinary and incomplete moments, probability weighted moments, cumulants and generating function, mean deviations, entropies and order statistics.
Keywords:
Beta-G model; Entropy; Mean deviation; Moment; Probability weighted moment; Regression model.
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Authors:Bentham Science Books