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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,Â¿,K) = 1 - (y - Â¿)Â¿K and the limited distribution F2(x,Â¿,K) = 1 - (Â¿ - x)K by a simple transformation of the corresponding estimator of the scale parameter of the exponential distribution Â¿Â¿mn, based on the first m order statistics of a sample of size n. Use is made of the fact that KÂ¿mn|Â¿ = 1/Â¿Â¿mn and KÂ¿mn|Â¿ = 1/Â¿Â¿mn, where 2mÂ¿mn/Â¿ 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 KÂ¿mn|Â¿ and KÂ¿mn|Â¿, which for a given m are the same for any n Â¿ m, are obtained by a simple transformation of that of Â¿Â¿mn. The expected values of KÂ¿mn|Â¿ and KÂ¿mn|Â¿ are determined and from them the unbiasing factors by which the ML estimators must be multiplied to obtain unbiased estimators KÂ¿mn|Â¿ and KÂ¿mn|Â¿. Expressions for the variances of the estimators and for the Cramer-Rao lower bound are found. A section on numerical examples is included.