Co ns id er a di screte probability di s tribution, re prese nte d by an n ·vector a . This pape r treats the probl em of adju stin g a as lillie as poss ible, in the se nse of minimizin g maxdxi -ad, to obtain a di s· tribution x whi ch sa ti sfi es gi ve n co mpon entwise bounds L .;; x ';; U , or a give n co mpone ntwi se ra nkin g, or both . The resultin g lin ea r programs are s hown to admit s pecial expli cit soluti on algorithms. Key word s: Lin ear programs; math e mati cal mode ls;

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... im ax es tim ation ; ope rations research; probabilit y d is tribution.