On moment measures of departure from the normal and exponential laws

For scale mixtures of distributions it is possible to prescribe simple moment measures of distance. In the case of departure from the normal and exponential laws of scale mixtures of the normal and exponential, these distances may be taken as the kurtosis and half the squared coefficient of variation minus one respectively. In this paper these measures of distance are exhibited as bounds on the uniform metric for the distance between distribution functions. The results considerably sharpen earlier results of a similar character in 2].