Abstract
This article obtains characterizations for the binomial. Grassia I-binomial, (carrier-borne epidemic). and randomized occupancy distributions via their factorial moments. The characierizing condition has the form:
d ln mu([r])'/db = theta(a, b, r)
where mu([r])' denotes the rth factorial moment. a and b are parameters. and theta(a, b: r) is the ratio of two functions linear in r. Given support 0, 1,..., n. then the ratio mu([r])'/mu(2) is an ancillary statistic that is equal, greater than, or less than (n - 1)/n for the three distributions, respectively. The use of the ancillary statistic is demonstrated.
Original language | English |
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Pages (from-to) | 3059-3068 |
Number of pages | 10 |
Journal | Communications in Statistics: Theory and Methods |
Volume | 33 |
DOIs | |
Publication status | Published - 2004 |
Keywords
- characterization
- factorial moment
- binomial distribution
- Grassia binomial distribution
- Weiss distribution
- Carrier-borne epidemic
- randomized occupancy distribution
- specified occupancy distribution
- EPIDEMICS
- CARRIERS
- SPREAD