A statistical analysis of the lengths of grain-boundary and transgranular cracks induced during the initial straining of columnar-grain ice by a compressive load applied perpendicular to the long direction of the columns is presented. The analysis shows that the crack lengths are randomly distributed and form distinct but correlated populations. The lognormal distribution function is shown to be a good descriptor of the populations for 5-90% of their range. Statistical models are presented for the lognormal behaviour of the crack-length distribution and for the strain dependence of the crack density.The models assume that a change in the value of the random variable of the respective population depends on the population value of the variable at the time of the change. It is shown that the model for the strain dependence of the crack density is suitable for the strain dependence of the acoustic emission, measured in both columnar-grain and granular ice subject to constant compressive loads. Evidence is also presented for a lognormal dependence of the dislocation density on strain. The analysis demonstrates that the cracks that form during the initial straining of polycrystalline ice are independent, random events and that the resulting crack populations are precursors to failure by fracture.