Abstract
In some experimental situations it is necessary to estimate a proportion using several groups of cases where the sampling size is a random variable; the maximum likelihood estimator is then the ratio of two statistics, the number of occurrences of the event analyzed (X) and the overall sampling size (M). If the later is of Poisson type with parameter λ, a sequence of M=m Bernouilli trials originates a compound binomial-Poisson random variable. The estimator of the proportion p is studied within this framework, and a numerical approximation can be obtained for its sampling distribution for any sample size.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blyth, C. R. (1986) Approximate binomial confidence limits. J. Amer. Statist. Ass. 81, 843.
Blyth, C. R. and Still, H. A. (1983). Binomial confidence intervals. J. Amer. Statis. Ass. 78, 108.
Johnson, N. L. and Kotz, S. (1969) Discrete Distributions. Wiley-Interscience. New York.
Johnson, N.L., Kotz, S., Kemp, J. (1992) Discrete univariate distributions. Wiley, N.Y.
Katti, S. K. and Gurland, J. (1962). Some methods of estimation for the Poisson Binomial Distribution. Biometrics 18, 42, 51.
Shumway, R. and Gurland, J. (1960). Fitting the Poisson Binomial distribution. Biometrics 16, 522, 534.
Sprott, D. A. (1958). The Method of Maximum Likelihood applied to the Poisson Binomial distribution. Biometrics 14, 97, 106
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ocerin, J.M.C.y., Pérez, J.D. Point and interval estimators in a binomial-Poisson compound distribution. Statistical Papers 43, 285–290 (2002). https://doi.org/10.1007/s00362-002-0101-3
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s00362-002-0101-3