Let Y∼GPN(μ,σ,p), then the transformed variable X=gpowerY;p has a truncated normal distribution TNμX,σ2,−1/p,∞ if p>0, TNμX,σ2,−∞,−1/p if p<0 and normal distribution NμX,σ2 if p=0 with μX=gpower(μ,p).