Asymptotic distribution of the random vector of differences between theoretical probabilities and their estimates, based on the sample quantiles and on an estimate of the unknown parameter, is derived in a setting not requiring differentiability of the densities. By means of this result asymptotically chi-square distributed goodness-of-fit test statistics are constructed for the exponential distribution and for the Laplace distribution.
93E25, 93C99, 93E11