Before revision:  Our approximations are motivated by  extensions of the so-called Normal Power Approximation, used for approximating the cumulative distribution function of a random variable, incorporating not only the skewness but the kurtosis of the random variable in question as well.
After revision:  Our approximations are motivated by extensions of the so-called Normal Power Approximation, used for approximating the cumulative distribution function of a random variable, which incorporate not only the skewness but the kurtosis of the random variable in question as well.