Modelling the FFDA fibre diameter histogram of fleece wool as a mixture distribution

Abstract

The histogram of wool fibre diameters obtained by processing fleece samples through the Fibre Fineness Distribution Analyser (FFDA) machine is modelled as a mixture of two normal distributions fitted on the log scale (model iv). The paper compares this model with a single normal distribution on the natural scale (model i), a single normal distribution on the log scale (model ii) and a mixture of two normal distributions on the natural scale (model iii). When fitted to 2544 fibre diameter histograms from Merino hoggets, these models gave average lack-of-fits, distributed as ¿225, of 549.6, 190.1, 93.5 and 39.5 for models i to iv respectively. Model iv is proposed as the basis for describing the FFDA fibre diameter histogram in sheep breeding.