ANALYSIS OF WEIGHT FREQUENCY-DISTRIBUTIONS USING REPLICATED DATA

The problem of analyzing weight frequency particle-size data is consid ered with respect to estimation of the sampling error of the size frac tions by weight. The established nonparametric method of Gy is reasses sed in terms of a general framework that allows simultaneous considera tion of both parametric and nonparametric approaches to the problem. T wo additional advantages result from introducing the present general f ramework. First, the formulas for the sampling variance of the sample size fraction by weight can be readily deduced from a general approach due to Scheaffer. Second, a fully parameteric approach can be develop ed for the case when a lognormal parametric model is appropriate for t he weight frequency distribution of the particles. For other parametri c models, an approximate parametric approach is indicated. For the non parametric case, an approach, alternative to Gy's, is also obtained. I n ah approaches developed in this article, replication data on the obs erved weight-frequency particle-size distribution is assumed to be ava ilable.