Distribution among sample test results when testing shelled corn lots for fumonisin

The statistical distribution known as the compound gamma function was studi ed for suitability in describing the distribution of sample test results as sociated with testing lots of shelled corn for fumonisin, Thirty-two 1.1 kg test samples were taken from each of 16 contaminated lots of shelled corn. An observed distribution consisted of 32 sample fumonisin test results for each lot. The mean fumonisin concentration, c, and the variance, s(2), amo ng the 32 sample fumonisin test results along with the parameters for the c ompound gamma function were determined for each of the 16 observed distribu tions. The 16 observed distributions of sample fumonisin test results were compared with the compound gamma function using the Power Divergence test, The null hypothesis that the observed distribution could have resulted from sampling a family of compound gamma distributions was not rejected at the 5% significance level for 15 of the 16 lots studied, Parameters of the comp ound gamma distribution were calculated from the 32-fumonisin sample test r esults using the method of moments. Using regression analysis, equations we re developed that related the parameters of the compound gamma distribution to fumonisin concentration and the variance associated with a fumonisin te st procedure. An operating characteristic curve was developed for a fumonis in sampling plan to demonstrate the use of the compound gamma function.