Statistical Papers

, Volume 38, Issue 4, pp 409–421

A test for randomness of the environments in a branching process

  • Mohan Kale
  • T. V. Ramanathan

DOI: 10.1007/BF02925997

Cite this article as:
Kale, M. & Ramanathan, T.V. Statistical Papers (1997) 38: 409. doi:10.1007/BF02925997


This paper discusses an approximate score test for testing randomness of environments in a branching process without observing the environments. Using an appropriate martingale central limit theorem the asymptotic null distribution of test statistic is shown to be normal. When the offspring distribution is Poisson, the detail derivation of asymptotic distribution of the test statistic is presented.

Key words

Random environmentsbranching processMartingale central limit theoremscore test

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Mohan Kale
    • 1
  • T. V. Ramanathan
    • 1
  1. 1.Department of StatisticsUniversity of PunePuneIndia