Accession Number : AD0705637

Title :   ASYMPTOTIC DISTRIBUTIONS FOR SUMS OF INDEPENDENT EXPONENTIALLY DISTRIBUTED RANDOM VARIABLES AND FOR THE PURE BIRTH PROCESS.

Descriptive Note : Final rept.,

Corporate Author : ROCKETDYNE CANOGA PARK CALIF

Personal Author(s) : Sherman,Bernard

Report Date : JAN 1970

Pagination or Media Count : 16

Abstract : The question of asymptotic distributions for the pure birth process is considered. For the Poisson process it is known that the state variable x(t), appropriately standardized, converges in distribution to the normal distribution. For the Yule-Furry process the asymptotic distribution is exponential. The Poisson and Yule-Furry processes are the special cases, corresponding to alpha = 0 and alpha = 1, of the pure birth process x(t) with parameters lambda sub k = lambda (k to the power alpha), k = or > 1, minus infinity < alpha = or < 1, lambda a positive constant. On the basis of heuristic reasoning used in this report it is concluded that for this more general pure birth process the asymptotic distribution of the appropriately standardized state variable x(t) is normal if alpha = or < 1/2 and non-normal if 1/2 < alpha = or < 1.

Descriptors :   (*STATISTICAL DISTRIBUTIONS, RANDOM VARIABLES), EXPONENTIAL FUNCTIONS, STATISTICAL PROCESSES, SERIES(MATHEMATICS), CONVERGENCE

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE