Abstract: | Given \s{Xi, i 1\s} as non-stationary strong mixing (n.s.s.m.) sequence of random variables (r.v.'s) let, for 1 i n and some γ ε 0, 1], F1( x)=γ P( Xi< x)+(1-γ) P( Xi x) and Ii( x)=γ I( Xi< x)+(1-γ) I( Xi x) . For any real sequence \s{Ci\s} satisfying certain conditions, let .In this paper an exponential type of bound for P(Dn ), for any >0, and a rate for the almost sure convergence of Dn are obtained under strong mixing. These results generalize those of Singh (1975) for the independent and non-identically distributed sequence of r.v.'s to the case of strong mixing. |