ABSTRACT
To fix itleas, corisitlcr first the ~mivari;ttc c;tsc tl - 1; it is well-ltrrown that, if the 1alitloi11 vi~.riables X I , . . . , X N are ho~~iided, that is, if the density j has tlomain the finite interval l r ~ , , b] as opposed to I?, t l~eii the chiaracteristic fimction (71 will not satisfy the srr~ootl~licss Contlitioiis CJ1, C2, or C':.,. The sitlliltioli is cxcri~plifictl by the srnoothcsl ol s l~ch densities, r~i~rriely the uliiforrr~ density over thv irrtcrval [ - Q, tl] wtiose cl-~ar;tcteristic fimctiorl is given by @(S) = W; cf. Rao (1973, 11. 151).
