A simple maximum probability resolution algorithm for most probable numberanalysis using microsoft excel

摘要

Traditional most probable number (MPN) methods are executed using one of two schemes. The direct maximum probability resolution (DMPR) technique involves calculating the binomial probability distribution array, P (= IIi P-i; i dilutions), as a function of cell density (Delta) and finding the value of which corresponds to the maximum in P (the MPN). Alternatively, indirect MPR methods seek the solution to a nonlinear equation, related to Pi, by altering Delta. We describe herein a simple maximum probability resolution (SMPR) method of the second type which involves the repeated calculation (j cycles) of Delta (j+1) by the addition of a term, related to the partial first derivative of P-i, with respect to Delta, to Delta (j) until the MPN (Delta (final)) is reached. Using this SMPR algorithm and comparing our results with a DMPR procedure (n = 5, 10, or 96; 10,000 points per Pi), another indirect computer-based MPR method (n = 10 or 96), or published MPN tables (n = 5) we found that there was agreement to 3-5 significant figures. The SMPR approach also outperformed all other computer-based MPR techniques tested.