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- W1987596589 abstract "Use of the functional relationship between the exponential and the Pareto and limited distributions enables one to obtain conditional maximum-likelihood (ML) estimators, from singly censored samples, of the shape parameters of the Pareto distribution F1(y,?,K) = 1 - (y - ?)?K and the limited distribution F2(x,?,K) = 1 - (? - x)K by a simple transformation of the corresponding estimator of the scale parameter of the exponential distribution ??mn, based on the first m order statistics of a sample of size n. Use is made of the fact that K?mn|? = 1/??mn and K?mn|? = 1/??mn, where 2m?mn/? has the x2 distribution with 2m degrees of freedom, to set confidence bounds on the shape parameter K of the Pareto and limited distributions. The probability densities of K?mn|? and K?mn|?, which for a given m are the same for any n ? m, are obtained by a simple transformation of that of ??mn. The expected values of K?mn|? and K?mn|? are determined and from them the unbiasing factors by which the ML estimators must be multiplied to obtain unbiased estimators K?mn|? and K?mn|?. Expressions for the variances of the estimators and for the Cramer-Rao lower bound are found. A section on numerical examples is included." @default.
- W1987596589 created "2016-06-24" @default.
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- W1987596589 date "1969-05-01" @default.
- W1987596589 modified "2023-09-26" @default.
- W1987596589 title "Conditional Maximum-Likelihood Estimation, from Singly Censored Samples, of the Shape Parameters of Pareto and Limited Distributions" @default.
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- W1987596589 doi "https://doi.org/10.1109/tr.1969.5216981" @default.
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