The problem of estimating order-restricted scale parameters of two Gamma distributions is considered under the Pitman closeness criterion. A class of isotonic estimators including the MLE is proposed. Some properties of this class of isotonic estimators is given under the Pitman closeness...

Given two independent non-degenerate positive random variables X and Y, Lukacs (Ann Math Stat 26:319–324, <CitationRef CitationID="CR14">1955</CitationRef>) proved that X/(X + Y) and X + Y are independent if and only if X and Y are gamma distributed with the same scale parameter. In this work, under the assumption X/U and U are...</citationref>