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b(This)33 b(w)m(ould)g(follo)m(w)e(from)g(the)i(follo)m(wing)d(simple)h(theorem:) 1872 5280 y Fm(2)p eop %%Page: 3 3 3 2 bop 0 83 a Fn(Theorem.)55 b Fb(A)36 b(discrete)h(stable)f Fo(\()p Fk(\025;)17 b(\015)5 b Fo(\))36 b Fb(random)f(v)-5 b(ariable)35 b(is)h(distributed)g(as)g(a)g(P)m(oisson)h(random)0 216 y(v)-5 b(ariable)45 b(with)i(parameter)f Fk(\025)1154 180 y Fg(1)p Fj(=\015)1269 216 y Fk(S)1329 231 y Fj(\015)t(;)p Fg(1)1428 216 y Fb(,)51 b(where)d Fk(S)1862 231 y Fj(\015)t(;)p Fg(1)2008 216 y Fb(is)e(a)h(p)s(ositiv)m(e)f(stable)g(random)g(v)-5 b(ariate)46 b(with)0 349 y(parameter)32 b Fk(\015)5 b Fb(:)1274 496 y Fk(X)j Fo(\()p Fk(\025;)17 b(\015)5 b Fo(\))1636 440 y Ff(L)1623 496 y Fo(=)27 b(P)m(oisson)q(\()p Fk(\025)2141 455 y Fg(1)p Fj(=\015)2255 496 y Fk(S)2315 511 y Fj(\015)t(;)p Fg(1)2415 496 y Fo(\))32 b Fk(:)0 998 y Fn(Pr)n(oof.)56 b Fo(W)-8 b(e)33 b(recall)e(that)h Fk(S)1098 1013 y Fj(\015)t(;)p Fg(1)1230 998 y Fo(has)h(c)m (haracteristic)f(function)1504 1195 y Fk(')p 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y(M.)j(Kan)m(ter,)g(\\Stable)f(densities)h (under)h(c)m(hange)g(of)e(scale)h(and)g(total)e(v)-5 b(ariation)31 b(inequalities,")h Fb(An-)0 5053 y(nals)g(of)g (Probabilit)m(y)p Fo(,)f(v)m(ol.)h(3,)h(pp.)g(697{707,)e(1975.)1872 5280 y Fm(5)p eop %%Page: 6 6 6 5 bop 0 94 a Fo(Y)-8 b(u.)27 b(V.)h(Linnik,)e(\\Linear)g(forms)h(and) g(statistical)e(criteria:)h(I,)h(I)s(I,")g Fb(Selected)h(T)-8 b(ranslations)27 b(in)f(Math-)0 227 y(ematical)k(Statistics)i(and)h (Probabilit)m(y)p Fo(,)e(v)m(ol.)h(3,)g(pp.)h(1{40,)f(41-90,)f(1962.)0 426 y(G.)48 b(Marsaglia,)f(\\The)i(squeeze)i(metho)s(d)d(for)g (generating)g(gamma)f(v)-5 b(ariates,")47 b Fb(Computers)j(and)0 559 y(Mathematics)32 b(with)g(Applications)p Fo(,)f(v)m(ol.)h(3,)h(pp.) g(321{325,)e(1977.)0 758 y(D.)43 b(Le)g(Minh,)g(\\Generating)e(gamma)g (v)-5 b(ariates,")42 b Fb(A)m(CM)j(T)-8 b(ransactions)43 b(on)g(Mathematical)e(Soft-)0 891 y(w)m(are)p Fo(,)33 b(v)m(ol.)g(14,)f(pp.)h(261{266,)e(1988.)0 1090 y(A.)i(P)m(ak)m(es,)h 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b(of)g(the)h(Institute)g(of)f(Statistical)e(Mathematics) p Fo(,)i(v)m(ol.)h(33,)f(pp.)h(177{190,)e(1981.)0 2751 y(E.)55 b(Stadlob)s(er,)e(\\The)i(ratio)e(of)h(uniforms)f(approac)m(h)i (for)e(generating)h(discrete)h(random)e(v)-5 b(ari-)0 2883 y(ates,")33 b Fb(Journal)f(of)g(Computational)e(and)i(Applied)g (Mathematics)p Fo(,)g(v)m(ol.)h(31,)f(pp.)h(181{189,)e(1990.)0 3083 y(F.)36 b(W.)g(Steutel)h(and)f(K.)g(V)-8 b(an)36 b(Harn,)h(\\Discrete)f(analogues)f(of)h(self-decomp)s(osabilit)m(y)d (and)k(stabil-)0 3215 y(it)m(y)-8 b(,")32 b Fb(Annals)g(of)h (Probabilit)m(y)p Fo(,)d(v)m(ol.)j(7,)f(pp.)h(893{899,)e(1979.)0 3415 y(V.)44 b(M.)g(Zolotarev,)f Fb(One-Dimensional)e(Stable)i (Distributions)p Fo(,)f(American)h(Mathematical)f(So)s(ci-)0 3548 y(et)m(y)-8 b(,)34 b(Pro)m(vidence,)g(R.I.,)e(1986.)1872 5280 y Fm(6)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF