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<jats:p>Faddy (1990) has conjectured that the variability of a pure birth process is increased, relative to the linear case, if the birth rates are convex and decreased if they are concave. We prove the conjecture by relating variability to the correlation structure of certain more informative versions of the process. A correlation inequality due to Harris (1977) is used to derive the necessary positive and negative correlation results.</jats:p>

Original publication

DOI

10.2307/3214838

Type

Journal article

Journal

Journal of Applied Probability

Publisher

Cambridge University Press (CUP)

Publication Date

06/1993

Volume

30

Pages

275 - 284