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

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, a(i) could be equal to i for all i. Let X(1n) < or = X(2n) < or = ... < or = X(nn) 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 k(2 < or = k < or = n), independence of the event (X(kn) = X(1n)), and X(1n) is equivalent to X being either degenerate or geometric.

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1978
Accession Number
ADA051094

Entities

People

  • Emad El-neweihi
  • Z. Govindarajulu

Organizations

  • University of Kentucky

Tags

DTIC Thesaurus Topics

  • Computing-Related Activities
  • Data Science
  • Information Science
  • Interdisciplinary Science
  • Mathematics
  • Numbers
  • Order Statistics
  • Random Variables
  • Real Numbers
  • Statistical Samples
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.