Moments Formulas for (X/m).
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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Let X be an integer-valued random variable. Let m be a given integer 1 and let Xm denote the greatest integer or Xm. The authors provide formulas for characteristics of the distribution of Xm 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
- Statistics and Probability