# Accession Number:

## AD0692526

# Title:

## SOME CONTRIBUTIONS TO MULTIPLE DECISION (SELECTION AND RANKING) PROCEDURES,

# Descriptive Note:

# Corporate Author:

## PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1969-08-01

# Pagination or Media Count:

## 133.0

# Abstract:

Let Pi sub i,i1,...,k, be a continuous population with associated distribution function F sub lambda sub i, lambda sub i epsilon Lambda an interval on the real line. Chapter I defines a class of procedures for selecting a non-empty subset of the k populations, such that the probability of a correct selection PCS, i.e. selection of a subset which includes the population with the largest smallest lambda sub i, is at least P, a preassigned level. A generalization of a result of Lehmann is used to obtain a sufficient condition for the monotonicity of a probability integral leading to the evaluation of the infimum of PCS over the parameter space. Results concerning the supremum of the expected subset size are obtained. More specific results are obtained when the density f sub lambda x is a convex mixture of a sequence of known density functions. The next chapter examines the selection from multivariate normal populations in terms of multiple correlation coefficient and illustrates the applications of the results of Chapter I. In Chapter III, a partial ordering h-ordering is defined on the space of probability distributions and selection from populations h-ordered w.r.t. a known distribution G is discussed. The last chapter briefly discusses some possible variations in the goal and the procedures. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability