Modelling the number of olive groves in Spanish municipalities

Abstract

The univariate generalized Waring distribution (UGWD) is presented as a new model to describe the goodness of fit, applicable in the context of agriculture. In this paper, it was used to model the number of olive groves recorded in Spain in the 8,091 municipalities recorded in the 2009 Agricultural Census, according to which the production of oil olives accounted for 94% of total output, while that of table olives represented 6% (with an average of 44.84 and 4.06 holdings per Spanish municipality, respectively). UGWD is suitable for fitting this type of discrete data, with strong left-sided asymmetry. This novel use of UGWD can provide the foundation for future research in agriculture, with the advantage over other discrete distributions that enables the analyst to split the variance. After defining the distribution, we analysed various methods for fitting the parameters associated with it, namely estimation by maximum likelihood, estimation by the method of moments and a variant of the latter, estimation by the method of frequencies and moments. For oil olives, the chi-square goodness of fit test gives p-values of 0.9992, 0.9967 and 0.9977, respectively. However, a poor fit was obtained for the table olive distribution. Finally, the variance was split, following Irwin, into three components related to random factors, external factors and internal differences. For the distribution of the number of olive grove holdings, this splitting showed that random and external factors only account about 0.22% and 0.05%. Therefore, internal differences within municipalities play an important role in determining total variability.Additional key words: table olive; oil olive; agricultural holdings; Waring distribution; estimation. Abbreviations used: L (liability); MF12 (method of one equation of moments and two relations between frequency); MF21 (method of two relations between moments and one equation of frequency); MLE (method of log-likelihood optimisation); MM3 (method of the three relations between moments); P (proneness); R (randomness); UGWD (Univariate Generalized Waring Distribution).

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

“…Later, Irwin (1968) used these data to improve the fit through univariate generalized Waring distribution. Since then, Mathematics 2020, 8, 2025 3 of 11 the Waring distribution has been used, in addition to the theory of accidents [15,26], in other fields such as biology [27], reliability theory [26], library science [28], computer science [29], psychiatry [30], medicine [31], linguistics, economics [32] and agriculture [33]. However, in this research it is applied in studies related to livestock, which has never been done.…”