Abstract. We present a concept of lower generalized order statistics. With this definition we give recurrence relations for single and product moments of lower generalized order statistics from the inverse Weibull distribution.

We extend and generalize some recent results on complete convergence (cf. Hu, Moricz, and Taylor [14], Gut [ll], Wang, Bhaskara Rao, and Yang [26], Kuczmaszewska and Szynal 1171, and Sung [23]) for arrays of rowwise independent Banach space valued random elements. In the main result, no assumptions are made concerning the existence of expected values or absolute moments of the random elements and no assumptions are made concerning the geometry of the underlying Banach space. Some well-known results from the literature are obtained easily as corollaries. The corresponding convergence rates are also established. 963

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