Details

Autor(en) / Beteiligte

• Waugh, W. A. O'N.

Titel

Transformation of a Birth Process Into a Poisson Process

Ist Teil von

• Journal of the Royal Statistical Society. Series B, Methodological, 1970-01, Vol.32 (3), p.418-431

Ort / Verlag

London: Royal Statistical Society

Erscheinungsjahr

1970

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The pure birth process with linear birth rates is considered. The sum of sojourn times is shown to have a functional relationship with an asymptotic estimate of the population size that is known from the theory of branching processes. A theorem concerning this estimate, due to Kendall (1966), is proved by means of this relationship, in a way which brings out the connection between Kendall's theorem and an important property of non-time-homogeneous Poisson processes. Further developments are then studied. An alternative way to generate the birth process is described. This brings in certain conditioned processes, the condition being the value of the asymptotic estimate just mentioned. Rates of convergence to the asymptotic value are also considered.