Descriptive statistics and analysis of interval symbolic data with general distribution
Feng Gao · Systems Engineering - Theory & Practice · 2011
Interval symbolic data gained by data packaging on the original individuals of a sample are subjects of this paper.The individuals are always non-uniformly distributed within the intervals.Regarding this situation,this paper concentrates on descriptive statistics and analysis of generally distributed interval data,within which each individual is arbitrarily distributed.The basic theory of symbolic data analysis was first introduced.Then the definition of generally distributed interval was proposed.In the following,the study on empirical distribution function and empirical joint distribution function for generally distributed interval symbolic data were put forward.Based on this,the descriptive statistics of generally distributed interval variables were obtained.Finally a numerical example was given.And an application study in Chinese stock market was carried through using factor analysis of generally distributed interval symbolic data.Research shows that the previous works supposing uniform distribution are especial case of this work. Besides this,the method presented in this paper does not need the exact form of distribution function, since it is obtained upon theory of empirical distribution.Furthermore,it makes the best of the individuals sample information of the intervals.