Moments Formulas for (X/m).
Abstract
Let X be an integer-valued random variable. Let m be a given integer > 1 and let (X/m) denote the greatest integer < or = X/m. The authors provide formulas for characteristics of the distribution of (X/m) expressed in terms of characteristics of the distribution of X. Exact formulas are given for the characteristic function and moments, and useful approximations are introduced and analyzed. The motivating application, in which X plays the role of number of events of a Poisson series in a fixed time interval, is dealt with in Section 4. The formulas utilized there are derived in general form in Section 2, and analysis is carried out in both Sections 2 and 3. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1971
- Accession Number
- AD0730458
Entities
People
- I. R. Savage
- Robert Serfling
Organizations
- Florida State University