Estimation of number of degrees of freedom of nuclear reaction widths distributions

Abstract

The effects of sinall sample sizes have been studied in estimating the number of degrees of freedom of nuclear reaction widths distributions using the method of nlaxinlum likelihood, the method of moments, and the method of minimization of variance. It is found that the estimates are biased a s a function of the sample size and the number of degrees o f freedom of the widths distribution. Bias is reduced somewhat by applying the estimation techniques t o the finite sample transforn~ation of the chi-squared distribution, the beta distribution. T h e efficiency of each estimation technique is indicated by comparison of the variances of the estimates t o the mininlum variance obtainable. A modified maxinlunl likelihood estimator is found t o be unbiased and efficient.