January 1943
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69 Citations
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... The historical origin of this class of problems is to be found in early work of the Italian school of probability like Gini (1914) [31], Salvemini (1949) [78], Dall'Aglio (1956) [20], as well as by Fréchet (1940Fréchet ( , 1951 [27,28], Hoeffding (1940Hoeffding ( , 1951 [32,33], who established upper and lower bounds for a distribution function F of n variables, when marginals F F ,…, n 1 are prescribed as well as sharp upper and lower bounds in the real case = n 2 for EX X 1 2 with X F i i , = i 1, 2. An extension to bounds for ( ) Eφ X X , 1 2 for supermodular functions φ was given in Cambanis et al. (1976) [17], Whitt (1976) [85], Szulga (1978) [81], Tchen (1980) [82]. A general formulation of this class of topics was introduced in Rüschendorf (1979Rüschendorf ( , 1980Rüschendorf ( , 1983 [63,64,66] and Gaffke and Rüschendorf (1981), [65] in general (multimarginal) context as generalized Hoeffding-Fréchet functionals defined for probability measures m φ M φ , describes the range of values caused by dependence. ...
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January 1943