We calculate the higher order moments in a sequence of models where the initial density fluctuations are drawn from a \chi ^ { 2 } _ { \nu } distribution with a power-law power spectrum .
For large values of \nu the distribution is approximately gaussian , and we reproduce the values known from perturbation theory .
As \nu is lowered the distribution becomes progressively more non-gaussian , approximating models with rare , high-amplitude peaks .
The limit \nu = 1 is a realization of recently proposed isocurvature models for producing early galaxy formation where the density perturbations are quadratic in a gaussian field .