The next theorem gives the main property of gpower-normal variables: after a gpower transformation they become truncated normals (TN). Recall that if X is a TN variable, its density is given by fXx,μX,σ2=1K12πσexp−12x−μXσ2Ia,b, where I is the indicator function, a,b=−1/p,∞ifp>0, a,b=−∞,∞ifp=0 and a,b=−∞,−1/pifp<0; μX∈R and we will denote that X∼TNμX,σ2,a,b (see Dhrymes [13]).