# Accession Number:

## ADA051094

# Title:

## Characterizations of Geometric Distribution and Discrete IFR (DFR) Distributions Using Order Statistics.

# Descriptive Note:

## Interim rept.,

# Corporate Author:

## KENTUCKY UNIV LEXINGTON DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1978-01-01

# Pagination or Media Count:

## 11.0

# Abstract:

Let X be a discrete random variable the set of possible values finite or infinite of which can be arranged as an increasing sequence of real numbers a1 a2 a3 ... . In particular, ai could be equal to i for all i. Let X1n or X2n or ... or Xnn denote the order statistics in a random sample of size n drawn from the distribution of X, where n is a fixed integer or 2. Then, it is shown that for some arbitrarily fixed k2 or k or n, independence of the event Xkn X1n, and X1n is equivalent to X being either degenerate or geometric.

# Descriptors:

# Subject Categories:

- Statistics and Probability