Box-Cox Transformation for Resolving the Peelle's Pertinent Puzzle in a Curve Fitting

摘要

Incorporating the Box-Cox transformation into a curve fitting is presented as one of methods for resolving an anomaly known as the Peelle's Pertinent Puzzle in the nuclear data community. The Box-Cox transformation is a strategy to make non-normal distribution data resemble normal distribution data. The proposed method consists of the following steps: transform the raw data to be fitted with the optimized Box-Cox transformation parameter, fit the transformed data using a conventional curve fitting tool, the least-squares method in this study, then inverse-transform the fitted results to the final estimates. Covariance matrices are correspondingly transformed and inverse-transformed with the aid of the law of error propagation.rnIn addition to a sensible answer to the Puzzle, the proposed method resulted in reasonable estimates for a test evaluation with pseudo-experimental 6Li(n,t) cross sections in several to 800 keV energy region, while the GMA code resulted in systematic underestimates that characterize the Puzzle. Meanwhile, it is observed that the present method and the Chiba-Smith method yield almost the same estimates for the test evaluation on 6Li(n,t). Conceptually, however, two methods are very different from each other and further discussions are needed for a consensus on the issue of how to resolve the Puzzle.