Within a population of shelled peanuts, aflatoxin may be concentrated in less than 0.5% of the peanuts. Those peanuts containing aflatoxin might have concentrations up to 1,000,000 µg of aflatoxin per kilogram of peanuts. Because of the distribution pattern, sample means vary widely, and the true average level of aflatoxin in the population is difficult to estimate. The objective of this study was to determine the effect of sample size, N, on sampling accuracy. The negative binomial distribution of aflatoxin since it allowed for a high probability of zero counts along with small probabilities of large counts. Using both the Monte Carlo technique and a direct computation method, the effect of sample size on sampling accuracy was quantitatively described.
Suitability of the negative binomial distribution for use in estimating the probabilities associated with sampling lots of shelled peanuts for aflatoxin analysis has been studied. Large samples, called "minilots," were drawn from 29 lots of shelled peanuts contaminated with aflatoxin. These minilots were subdivided into ca. 12 lb samples which were analyzed for aflatoxin. The mean and variance of these aflatoxin determinations for each minilot were determined. The shape parameter k and the mean aflatoxin concentration m were estimated for each minilot. A regression analysis indicated the functional relationship between k and rn to be: k = (2.0866 + 2.3898m) x 10 -6. The observed distribution of sample concentrations from each of the 29 minilots was compared to the negative binomial distribution by means of the Kolmogorov-Smirnov test. The null hypothesis that each of the true unknown distribution functions was negative binomial was not rejected at the 5% significance level for all 29 comparisons. .2 aTest results are given in ppb aflatoxin and are ordered according to aflatoxin concentration.
Testing ABSTRACT A computer model that accounts for sampling, subsampling, and analytical variability was developed to simulate aflatoxin testing programs. Monte Carlo solution techniques were employed to account for conditional probabilities that arise from multiple samples, subsamples, and/or analyses being used in testing programs. The aflatoxin testing program to be used on the 1974 peanut crop was evaluated by use of the described model. lots with low test results and further testing of other lots. The additional tests may require that additional samples be drawn, that additional subsamples be analyzed, or that additional analyses be made on the same subsample. The conditional probabilities associated with this type of testing program cannot be handled by analytical means. This paper describes the development of a model coupled with Monte Carlo solution techniques to simulate aflatoxin testing programs, including those which involve conditional probabilities.
A number of modifications to the Markov chain probability model are proposed for cases in which the simple model does not fit sequences of wet or dry days, The modified models are shown to fit the observed records in most cases, and can also be applied to sequences of wet or dry hours. A solution to the problem of counting sequences within a limited time period is also given.
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