STATISTICAL PROPERTIES OF THE APPORTIONMENT DEGREE AND ALTERNATIVE MEASURES IN BUCKING OUTCOME

Resumen

ABSTRACT
In the harvesting technique prevailing in Scandinavia, tree stems are converted into smaller logs immediately at harvest. Modern sawmills attempt to operate according to customers' special needs rather
than only minimize the production costs. Since the annual production of saw timber in Scandinavia is in tens of millions of cubic meters, proper measuring of the goodness of the bucking outcome is of crucial importance. The outcome of the bucking operation can be considered as a multidimensional table of tree species, quality grades, prices and length and diameters classes. The prevailing method to measure the outcome is the so-called apportionment degree, which is calculated from the relative portions of the observed and target tables. However, this measure has severe drawbacks. E.g. it gives the same weight for each log class. Therefore, for example, the effect of the shape of the distributions is completely ignored. In this study we present some basic results of the statistical properties of the apportionment degree and
present some alternative means to measure the bucking outcome. Also a simulation study is carried out to illustrate the relative performance of the measures presented.

Key words: Apportionment degree, forest harvesting, frequency  Chi-Square, simulation.

RESUMEN
El propósito de este trabajo es comenzar el análisis estadístico del índice del prorrateo, esta es una medida usada en el contexto de la tala en bosques para evaluar el ajuste entre la demanda y distribución del suministro de la leña. Ha habido algunos esfuerzos por entender este índice, pero una base teórica seria todavía falta. Nosotros discutimos brevemente la literatura existente y procedemos a investigar las
propiedades del índice desde un punto de vista distribucional. Éste es fundamentalmente un artículo exploratorio y nosotros sólo enfocamos los casos de dos y tres clases de leña, es decir, locaciones. En el caso de dos clases usamos la distribución beta para las variables aleatorias relativas a la salida (output) del rendimiento; en tres locaciones al azar se asume que los rendimientos relativos siguen la distribución de Dirichlet singular. Usando esta formulación es posible entender las propiedades estadísticas del índice del prorrateo.