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

Abstract

Abstract 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 m to be: k =(2.0866+2.3898 m ) × 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.