Interval Estimation for the Poisson Distribution Parameter with a Single Observation

Juan Carlos Correa

 

Abstract       

The estimation of the parameter of the Poisson distribution, say λ , is an important task in applied statistics. Frequently we only have available a single observation and our goal is to construct a confidence interval. We illustrate under what conditions we can construct a confidence interval based on three methods: central limit theorem, exact method, and the likelihood ratio method. We also illustrate this problem constructing a confidence interval for the rate of suicides in Colombia.

 

Key words: Estimation, Confidence interval, Small sample size, Central limit theorem, Likelihood ratio.

 

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