Skip Navigation

Biometrika 1974 61(1):71-80; doi:10.1093/biomet/61.1.71
© 1974 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by KEIDING, N.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Estimation in the birth process

NIELS KEIDING

Institute of Mathematical Statistics, University of Copenhagen

Maximum likelihood estimation of the parameter {lambda} of a pure birth process is studied on the assumptions that the process is observed either continuously in a time interval [0, t] or at equidistant time points O, T, ..., KT. The exact distribution of the minimal sufficient statistic is given in the first case and for both cases the asymptotic theory as t-> {infty}, or as, k ->, {infty}, is studied. The related conditional Poisson process discussed recently by D. G. Kendall and W. A. O'N. Waugh is also studied, and the results are shown to illustrate the modern theory of exponential families and conditional inference.

Key Words: Conditional inference • Conditional Poisson process • Estimation in Markov processes • Exponential family • Maximum likelihood estimation • Point process • Pure birth process


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.