Abstract: | Summary LetX be a standard normal random variable and let σ be a positive random variable independent ofX. The distribution of η=σX is expanded around that ofN(0, 1) and its error bounds are obtained. Bounds are given in terms of E(σ
2V−σ
2−1)
k
whereσ
2Vσ
−2 denotes the maximum of the two quantitiesσ
2 andσ
−2, andk is a positive integer, and of E(σ
2−1)
k
, ifk is even.
The Institute of Statistical Mathematics |