Accession Number : AD0730458

Title :   Moments Formulas for (X/m).

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s) : Savage,I. R. ; Serfling,R. J.

Report Date : JUL 1971

Pagination or Media Count : 19

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)

Descriptors :   (*DISTRIBUTION FUNCTIONS, *STATISTICAL ANALYSIS), RANDOM VARIABLES, APPROXIMATION(MATHEMATICS), POWER SERIES, ASYMPTOTIC SERIES, STATISTICAL PROCESSES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE