<p>The motivating forestry background for this thesis is the need for fast, non-destructive, and cost-efficient methods to estimate fibre length distributions in standing trees in order to evaluate the effect of silvicultural methods and breeding programs on fibre length. The usage of increment cores is a commonly used non-destructive sampling method in forestry. An increment core is a cylindrical wood sample taken with a special borer, and the methods proposed in this thesis are especially developed for data from increment cores. Nevertheless the methods can be used for data from other sampling frames as well, for example for sticks with the shape of an elongated rectangular box.</p><p>This thesis proposes methods to estimate fibre length distributions based on censored mixture data from wood samples. Due to sampling procedures, wood samples contain cut (censored) and uncut observations. Moreover the samples consist not only of the fibres of interest but of other cells (fines) as well. When the cell lengths are determined by an automatic optical fibre-analyser, there is no practical possibility to distinguish between cut and uncut cells or between fines and fibres. Thus the resulting data come from a censored version of a mixture of the fine and fibre length distributions in the tree. The methods proposed in this thesis can handle this lack of information.</p><p>Two parametric methods are proposed to estimate the fine and fibre length distributions in a tree. The first method is based on grouped data. The probabilities that the length of a cell from the sample falls into different length classes are derived, the censoring caused by the sampling frame taken into account. These probabilities are functions of the unknown parameters, and ML estimates are found from the corresponding multinomial model.</p><p>The second method is a stochastic version of the EM algorithm based on the individual length measurements. The method is developed for the case where the distributions of the true lengths of the cells at least partially appearing in the sample belong to exponential families. The cell length distribution in the sample and the conditional distribution of the true length of a cell at least partially appearing in the sample given the length in the sample are derived. Both these distributions are necessary in order to use the stochastic EM algorithm. Consistency and asymptotic normality of the stochastic EM estimates is proved.</p><p>The methods are applied to real data from increment cores taken from Scots pine trees (Pinus sylvestris L.) in Northern Sweden and further evaluated through simulation studies. Both methods work well for sample sizes commonly obtained in practice.</p>

The motivating forestry background for this thesis is the need for fast, non-destructive, and cost-efficient methods to estimate fibre length distributions in standing trees in order to evaluate the effect of silvicultural methods and breeding programs on fibre length. The usage of increment cores is a commonly used non-destructive sampling method in forestry. An increment core is a cylindrical wood sample taken with a special borer, and the methods proposed in this thesis are especially developed for data from increment cores. Nevertheless the methods can be used for data from other sampling frames as well, for example for sticks with the shape of an elongated rectangular box. This thesis proposes methods to estimate fibre length distributions based on censored mixture data from wood samples. Due to sampling procedures, wood samples contain cut (censored) and uncut observations. Moreover the samples consist not only of the fibres of interest but of other cells (fines) as well. When the cell lengths are determined by an automatic optical fibre-analyser, there is no practical possibility to distinguish between cut and uncut cells or between fines and fibres. Thus the resulting data come from a censored version of a mixture of the fine and fibre length distributions in the tree. The methods proposed in this thesis can handle this lack of information. Two parametric methods are proposed to estimate the fine and fibre length distributions in a tree. The first method is based on grouped data. The probabilities that the length of a cell from the sample falls into different length classes are derived, the censoring caused by the sampling frame taken into account. These probabilities are functions of the unknown parameters, and ML estimates are found from the corresponding multinomial model. The second method is a stochastic version of the EM algorithm based on the individual length measurements. The method is developed for the case where the distributions of the true lengths of the cells at least partially appearing in the sample belong to exponential families. The cell length distribution in the sample and the conditional distribution of the true length of a cell at least partially appearing in the sample given the length in the sample are derived. Both these distributions are necessary in order to use the stochastic EM algorithm. Consistency and asymptotic normality of the stochastic EM estimates is proved. The methods are applied to real data from increment cores taken from Scots pine trees (Pinus sylvestris L.) in Northern Sweden and further evaluated through simulation studies. Both methods work well for sample sizes commonly obtained in practice.

Several researchers have concluded that there is little or no relationship between specific gravity and ring width or growth rate in yellow-poplar (Liriodendron tulipifera L.). Because most mechanical properties of wood are also closely related to specific gravity, it would thus be of interest to learn how minimum suppression and maximum release years' evidence that can be extracted from radial growth patterns based on a modified radial growth averaging (RGA) technique's influence the compression parallel to grain strength and specific gravity of wood. This study is designed to evaluate the effects of growth suppression and release on ultimate crushing stress and specific gravity for small-sized yellow-poplar specimens. Additionally, the relationship between specific gravity and ultimate crushing stress is investigated. Twenty-three yellow-poplar cores were examined for their growth ring widths. Minimum suppression and maximum release years were identified based on the modified RGA criteria method. From each increment core, three 1 Ã 1 Ã 4 mm specimens from both minimum suppression and maximum release years were tested for their ultimate crushing stresses using a micro-mechanical test system. The specific gravity of each specimen was also recorded. These data were analyzed using a paired samples t test and a simple linear regression. The results indicate that the mean ultimate crushing stress and specific gravity of maximum release years were significantly higher than that of minimum suppression years. Furthermore, the ultimate crushing stress was linearly related to the specific gravity of the specimens. / Master of Science