Interval data analysis based on empirical distribution function

Uniform distribution in some closed or tight interval is a basic assumption in the literature about interval data analysis, which is difficult to satisfy in real data processing. To solve this problem, the empirical cumulative distribution function (ECDF) and kernel estimation of cumulative distribution were studied, on the assumption that the date were from some continuous distribution. Based on ECDF and kernel estimation, a transformation to obtain new data was designed, which was uniformly distributed in theory. Then whether the distribution of transformed data was uniform distribution was tested. If the null hypothesis was not rejected, traditional methods in the field of interval data analysis could be utilized based on transformed data. The transform and the test were both for guaranteeing the transformed data were from some uniform distribution. Both simulation and real data example show that, the results based on ECDF and kernel estimation transformed data are more reasonable and with strong explanatory ability.