Characterizations of Geometric Distribution and Discrete IFR (DFR) Distributions Using Order Statistics.
KENTUCKY UNIV LEXINGTON DEPT OF STATISTICS
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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.
- Statistics and Probability