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