MEAN SQUARE INVARIANT FORECASTERS FOR SOME WEIBULL DISTRIBUTIONS.
COLUMBIA UNIV NEW YORK SCHOOL OF ENGINEERING AND APPLIED SCIENCE
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Given n initial observations constituting a sequence drawn from a set X1, ... , Xn, of n independent and identically distributed random variables with the Weibull distribution known shape parameter, a mean square invariant forecaster has been found for the expected minimum maximum of a subsequent sequence of the next m observations. When the location parameter instead of the shape parameter is known, reduction to the Gumbel distribution is immediate and the same technique again gives an invariant forecaster. The formulae, although amenable to computation, are cumbersome.
- Theoretical Mathematics