Statistical inference on the Poisson rates when only the ordered markings are available

Research Report SRR95-036

Statistical inference on the Poisson rates when only the ordered markings are available

Kee-Won Lee

Abstract: Statistical methods are proposed for conducting an inference on the rate of a Poisson distribution when the data are recorded in such a way that only the frequencies of ordered markings are available. Maximum likelihood methods and minimum chi-square methods are used to estimate the unknown rate of occurrences. Traditional asymptotic methods and bootstrap methods are used in the computation of the standard error of the estimated rate, producing similar results. One sample and two sample cases are considered for hypothesis testing. Traditional asymptotic methods and bootstrap methods are used to approximate the achieved significance level for various test statistics. An example from pathology lab test data is explored to illustrate the feasibility of the proposed methods.

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