In this paper we clarify the relationship between the relaxation rate and relaxation time distributions underlying the Kohlrausch-Williams-Watts (KWW) photoconductivity build-ups in indium- and gallium-doped Cd(1-x)Mn(x)Te mixed crystals. We discuss the role of asymptotic properties of the corresponding probability density functions. We show that the relaxation rate distribution, as a completely asymmetric α-stable distribution, leads to an infinite mean value of the effective relaxation rate. In contrast, the relaxation time distribution related to it leads to a finite mean value of the effective relaxation time. It follows from the experimental data analysis that for all the investigated samples the KWW exponent α decreases linearly with increasing photon flux in the range of (0.6-0.99) and its values are more spread in the case of gallium-doped material. We also observe a linear dependence of the mean relaxation time on the characteristic material time constant, which is consistent with the theoretical model.