  Recently, the characterization based approach for the construction of
goodness of fit tests has become popular. Most of the proposed tests have been
designed for complete i.i.d. samples. Here we present the adaptation of the
recently proposed exponentiality tests based on equidistribution-type
characterizations for the case of randomly censored data. Their asymptotic
properties are provided. Besides, we present the results of wide empirical
power study including the powers of several recent competitors. This study can
be used as a benchmark for future tests proposed for this kind of data.
