Minimax Error Selection of a Univariate Distribution With Prescribed Componentwise Bounds and Ranking

Abstract

The top ic treated is that of fi nding a re producib le, plaus ible and computationall y s imple method of selecting a di screte frequency di s tribution with a prescr ib ed rankin g of its components and pre· scrib ed upper and lowe r bounds on these compone nt. s . The problem is s hown to be tract.ab le when a minimax error selection c rit e ri on is e mployed, and "error " is measure d by maximum absolut e devia­ ti on a mong co mpone nts. In thi s case one obt.ains a lin ea r progra m of a specia l form ad mittin g expli c it solutio n.