Abstract
Suppose that the minimum of a pair of independent non-negative random variables X and y has the same distribution, up to a scale factor, as the first of the two random variables. The restricted class of possible distributions for X and Y is identified. If in addition it is required that X and Y have distributions only differing by a scale factor, it is shown under mild regularity conditions that X and Y have Weibull distributions.
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Arnold, B.C., Isaacson, D. On solutions to min \((X,{\text{ Y}})\mathop = \limits^d aX\) and min \((X,{\text{ Y}})\mathop = \limits^d aX\mathop = \limits^d bY\) . Z. Wahrscheinlichkeitstheorie verw Gebiete 35, 115–119 (1976). https://doi.org/10.1007/BF00533315
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DOI: https://doi.org/10.1007/BF00533315