Comparison of the observed distribution of aflatoxin in shelled peanuts to the negative binomial distribution

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 parameterk and the mean aflatoxin concentrationm were estimated for each minilot. A regression analysis indicated the functional relationship betweenk andm to be:k=(2.0866+2.3898m) × 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. Journal Series Paper of the North Carolina State University Agricultural Experiment Station, Raleigh, N.C.