The Waring Distribution as a Low-Frequency Prediction Model: A Study of Organic Livestock Farms in Andalusia

Abstract

Although the numbers are relatively small with respect to non-organic livestock, the importance of organic livestock farms lies in their sustainable coexistence with the natural environment and in the high-quality food products obtained. In this type of production, no artificial chemicals or genetically modified organisms are used, therefore there will be less impact on the environment and, in most cases, native breeds are employed. This paper describes a geostatistical study of organic livestock farms in Andalusia (southern Spain), conducted using information from the 2009 Agricultural Census, by classes of livestock. This region currently records the highest output in Spain for organic livestock farming. The number of farms was fitted according to the univariate generalized Waring distribution, which is presented as a means of analyzing this type of discrete measurement, using agricultural or livestock data. The Waring distribution is used when the frequency of occurrence of a phenomenon is very low and allows one to divide the variance. The most important outcome of this study is the finding that livestock data variability is mainly due to external factors such as the proneness component of the variance.