Abstract
An useful and interesting characterization of the Weibull distribution is its lack of memory (of order α) property, i.e., P(X ≥ (xα + yα)1/α|X ≥ y) = P(X ≥ x) for all x, y ≥ 0. The characterization holds even in the case when it is required to fulfil this relation not on the entire semi-axis {y|y ≥ 0}, but only at two incommensurable points y1 and y2. The stability estimation in this characterization is analyzed.
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