# Accession Number:

## ADA052314

# Title:

## Asymptotic Behavior of Intermediate Order Statistics: The Infinite Endpoint Case.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1977-10-01

# Pagination or Media Count:

## 14.0

# Abstract:

Suppose X1, X2, ... is a sequence of independent and identically distributed random variables with marginal distribution function Fx PX1 or x satisfying Fx 0 for all real x. Let Xk sub n superscript n denote the k sub nth smallest order statistic of the sample X1, ..., Xn, where k sub nn approaches 0 as n approaches infinity. An almost sure representation of Xk sub n superscript n in terms of the empirical distribution function is established. The conditions imposed upon F include those under which it is known that Xk sub n superscript n is asymptotically normal. From the representation the law of the iterated logarithm for Xk sub n superscript n is obtained. Examples illustrating the general result are presented. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability