 The parameter formula_19 is in this case imaginary, but the function formula_7 is nevertheless real, positive, and normalizable.The scale parameter formula_3 of the "canonical" normal distribution must be positive because the distribution would not be normalizable otherwise.The doubly truncated normal distribution, on the other hand, can in principle have a negative scale parameter (which is different from the variance, see summary formulae), because no such integrability problems arise on a bounded domain.