A Note on the Ratio of Two Independent Random Variables

Abstract

It is well known that the k-dimension simnplex (Triangle, Tetrahedron, etc.) provides a minimum location design for a first order polynomial in k variables. It does not appear to have been observed that the corresponding series of polyhedral arrays provide iminimum location designs for rlh order polynomials in k variables. If we label one set of diagonals in Pascal's triangle as the number of variables and the other set as the order of the polynomial then the intersection of the k and r diagonals gives the polyhedral array for the rtll order polynomial in k variables. Design coordinates can be conveniiently constructed as an allocation problem as in the following example. The permutations of each allocation provide the coordinates of the design locations. Example: 4th Order in 4 Variables Allocation Permutations