  Information collection is a fundamental problem in big data, where the size
of sampling sets plays a very important role. This work considers the
information collection process by taking message importance into account.
Similar to differential entropy, we define differential message importance
measure (DMIM) as a measure of message importance for continuous random
variable. It is proved that the change of DMIM can describe the gap between the
distribution of a set of sample values and a theoretical distribution. In fact,
the deviation of DMIM is equivalent to Kolmogorov-Smirnov statistic, but it
offers a new way to characterize the distribution goodness-of-fit. Numerical
results show some basic properties of DMIM and the accuracy of the proposed
approximate values. Furthermore, it is also obtained that the empirical
distribution approaches the real distribution with decreasing of the DMIM
deviation, which contributes to the selection of suitable sampling points in
actual system.
