Abstract： Selective model provided a way to explain the generation of index law and power law on the basis of preferential probability analysis. A transformation formula between the selective scope rule and selective distribution was deduced through the research on preferential trials. It was named as preferential transformation, which offered a mean to study the rule of monotone distributions. A corresponding continuous transformation can be deduced by the preferential transformation for analyzing probability density function. Compared with the discrete distribution, we defined a comparison function for continuous distribution, and pointed out the relationship between the discrete distribution and continuous distribution. Through selective model, we simulated and analyzed the power law phenomena. Selective theory was important to the research on huge complex system and social behavior. It could also expand the foundation of statistical physics and probability theory.
selective modelpower law phenomenapreferential transformationcomparison function