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- W411906871 abstract "S ummary Under what conditions does the distribution of the maximum of a set of independent random variables uniquely determine the distributions of the component random variables? In the univariate case, a sufficient condition is that for every pair of distinct densities in the family of possible densities, one density converges to zero infinitely faster than the other, as x → ∞. Hence, the distribution of max { X i , i = 1, ..., n } when X i has the distribution N (μ i , σ 2 i ), uniquely determines μ i , σ 2 i , i = 1, ..., n (except for indexing). The identifiability property is proved for bivariate normal distributions for every n when all correlations are positive; each component of the vector of maxima consists of the maximum of that component of the n constituent vectors." @default.
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- W411906871 date "1977-07-01" @default.
- W411906871 modified "2023-09-26" @default.
- W411906871 title "Identification of Parameters by the Distribution of a Maximum Random Variable" @default.
- W411906871 doi "https://doi.org/10.1111/j.2517-6161.1977.tb01632.x" @default.
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