1Universidad de Valparaíso, Departamento de Estadística, Valparaíso, Chile. Professor. Email: victor.leiva@uv.cl
2Universidad de Talca, Instituto de Matemáticas y Física, Talca, Chile. Assistant profesor. Email: gponce@utalca.cl
3Universidad de Valparaíso, Departamento de Estadística, Valparaíso, Chile. Assistant profesor. Email: carolina.marchant@uv.cl ]]>
Mortality processes and the distribution of the diameter at breast height (DBH) of trees are two important problems in forestry. Trees die due to several factors caused by stress according to a phenomenon similar to material fatigue. Specifically, the force (rate) of mortality of trees quickly increases at a first stage and then reaches a maximum. In that moment, this rate slowly decreases until stabilizing at a constant value in the long term establishing a second stage of such a rate. Birnbaum-Saunders (BS) distributions are models that have received considerable attention currently due to their interesting properties. BS models have their genesis from a problem of material fatigue and present a failure or hazard rate (equivalent to the force of mortality) that has the same behavior as that of the DBH of trees. Then, BS distributions have arguments that transform them into models that can be useful in forestry. In this paper, we present a methodology based on BS distributions associated with this forest thematic. To complete this study, we perform an application of five real DBH data sets (some of them unpublished) that provides statistical evidence in favor of the BS methodology in relation to the forestry standard methodology. This application provides valuable financial information that can be used for making decisions in forestry.
Key words: data analysis, force of mortality, forestry, hazard rate.
Los procesos de mortalidad y la distribución del diámetro a la altura del pecho (DAP) de árboles son dos problemas importantes en el área forestal. Los árboles mueren debido a diversos factores causados por estrés mediante un fenómeno similar a la fatiga de materiales. Específicamente, la fuerza (tasa) de mortalidad de árboles crece rápidamente en una primera fase y luego alcanza un máximo, momento en el que comienza una segunda fase en donde esta tasa decrece lentamente estabilizándose en una constante en el largo plazo. Distribuciones Birnbaum-Saunders (BS) son modelos que han recibido una atención considerable en la actualidad debido a sus interesantes propiedades. Modelos BS nacen de un problema de fatiga de materiales y poseen una tasa de fallas (equivalente a la fuerza de mortalidad) que se comporta de la misma forma que ésa del DAP de árboles. Entonces, distribuciones BS poseen argumentos que las transforman en modelos que puede ser útiles en las ciencias forestales. En este trabajo, presentamos una metodología basada en la distribución BS asociada con esta temática forestal. Para finalizar, realizamos una aplicación con cinco conjuntos de datos reales (algunos de ellos no publicados) de DAP que proporciona una evidencia estadística en favor de la metodología BS en relación a la metodología estándar usada en ciencias forestales. Esta aplicación entrega información que puede ser valiosa para tomar decisiones forestales.
Palabras clave: análisis de datos, fuerza de mortalidad, silvicultura, tasa de riesgo.
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv35n3a02,
AUTHOR = {Leiva, Víctor and Ponce, M. Guadalupe and Marchant, Carolina and Bustos, Oscar},
TITLE = {{Fatigue Statistical Distributions Useful for Modeling Diameter andMortality of Trees}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2012}, ]]>
volume = {35},
number = {3},
pages = {349-370}
}