Comparing distributions with bootstrap techniques: An application to global solar radiation

A statistic to test whether the distributions of two observable variables are similar is proposed, where two distributions are defined as similar if they are the same except for a change in location and/or scale. The test statistic for similarity that is proposed extends the Kolmogorov–Smirnov statistic that is used to test for homogeneity of two samples, but it requires the use of a smooth bootstrap procedure to compute critical values. The application of the similarity test to the analysis of global solar radiation data from various Spanish regions reveals that the vast majority of distributions that can be compared are not homogeneous, but in many case there is no evidence to reject that they are similar. In practice, this implies that the use of prediction and simulation models that depend on global solar radiation data can be generalized to a wide variety of regions with almost no cost.