  We express the joint R\'enyi entropy of progressively censored order
statistics in terms of an incomplete integral of the hazard function, and
provide a simple estimate of the joint R\'enyi entropy of progressively Type-II
censored data. Then we establish a goodness of fit test statistic based on the
R\'enyi Kullback-Leibler information with the progressively Type-II censored
data, and compare its performance with the leading test statistic. A Monte
Carlo simulation study shows that the proposed test statistic shows better
powers than the leading test statistic against the alternatives with monotone
increasing, monotone decreasing and nonmonotone hazard functions.
