On the Probability of Survival of Bacteria in Sea Water

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Abstract
The observations consist of replicate "Most Probable Number" (MPN) estimates of bacterial densities [delta] t at fixed sampling times. To represent observed variability in replicate MPNs at each sampling time, a Gamma distribution of [delta]t is postulated and compounded with the binomial distribution of sterile tubes. Using a general formula for the factorial moments of such compound binomials, simple moment estimates of the parameters are obtained. These estimates are shown to be at least 95% as efficient as maximum likelihood estimates over a wide range of values of the parameters. The fitted compound distributions show good agreement with observed distributions of sterile tubes. Possible application of these results to problems in environmental sanitation are discussed.

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