Repeat the calculations of the previous exercise, this time for the exponential distribution in place of the Poisson. Compare numerically the transformation ±W1/2 with the Wilson-Hilferty cube root transformation 3n 1/2 {(

Y

μ0

)

1/3

+

1 9n − 1}, which is also normally distributed to a high order of approximation. Show that the cube root transformation has kurtosis of order O(n−1

), whereas ±W1/2 has kurtosis of order O(n−2

). For a derivation of the above result, see Kendall &

Stuart (1977, Section 16.7).

 P=869