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Biometrika 1991 78(2):295-299; doi:10.1093/biomet/78.2.295
© 1991 by Biometrika Trust
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Approximations to the maximum likelihood estimate in some pure birth processes

CHANGHYUCK OH1, NORMAN C. SEVERO2 and JOHN SLIVKA3

1Department of Statistics, YeungNam University KyungSan, KyungPook 714–749, South Korea
2Department of Statistics, State University of New York at Buffalo Buffalo, New York 14214, U.S.A.
3Department of Mathematics, State University College at Buffalo Buffalo, New York 14222, U.S.A.

We present two simple approximations, one an extension of that given by Choi & Severo (1988), to the maximum likelihood estimate of a parameter {lambda} in the class of birth processes in which the growth rate is the product of {lambda} and some known function of the population size. The data are population sizes taken at a discrete set of time points. The Yule process is discussed in some detail.

Key Words: Approximate maximum likelihood • Pure birth process • Yule process


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