Comparison of confidence intervals for the Poisson mean

Article type: Research Article

Authors: Patil, Dipak D.^{a; *} | Rajarshi, M. B.^b

Affiliations: [a] H.V. Desai College, Pune, India | [b] Department of Statistics, University of Pune, Pune, India

Correspondence: [*] Corresponding author: Dipak. D. Patil. E-mail: [email protected].

Abstract: Performance of various methods of confidence intervals for the mean of a Poisson distribution is evaluated in terms of coverage probability, expected length (width), p-confidence and p-bias. Methods include an exact procedure, methods based on normal approximations to pivotals, methods based on variance stabilizing transformation and five of these procedures with their bootstrap versions, in stead of the usual normal approximation. Comparison has been made by considering different values of Poisson mean and sample sizes. The nominal confidence coefficient has been taken to be 95%. Comparison is based on simulation studies. Recommendations for use of an appropriate method have been made as per requirements of a user.

Keywords: Bootstrap, confidence coefficient, confidence interval, p-bias, p-confidence, pivotal quantity, Poisson mean

DOI: 10.3233/MAS-2010-0145

Journal: Model Assisted Statistics and Applications, vol. 5, no. 2, pp. 79-91, 2010