A New Generalization of the Student’s t Distribution with an Application in Quantile Regression

In this work, we present a new generalization of the student’s t distribution. The new distribution is obtained by the quotient of two independent random variables. This quotient consists of a standard Normal distribution divided by the power of a chi square distribution divided by its degrees of freedom. Thus, the new symmetric distribution has heavier tails than the student’s t distribution and extensions of the slash distribution. We develop a procedure to use quantile regression where the response variable or the residuals have high kurtosis. We give the density function expressed by an integral, we obtain some important properties and some useful procedures for making inference, such as moment and maximum likelihood estimators. By way of illustration, we carry out two applications using real data, in the first we provide maximum likelihood estimates for the parameters of the generalized student’s t distribution, student’s t, the extended slash distribution, the modified slash distribution, the slash distribution generalized student’s t test, and the double slash distribution, in the second we perform quantile regression to fit a model where the response variable presents a high kurtosis.

Assessment of residual slash coverage using UAVs and implications for aspen regeneration

Proper redistribution of residual slash following harvesting is crucial for ensuring successful regeneration and continued health in trembling aspen (Populus tremuloides) forests. As traditional methods of measuring residual slash are a strenuous and tedious process, the objective of this study was to develop a new, faster, and more detailed method to assess residual slash distribution for entire harvested blocks. This study also aimed to assess the influence residual slash coverage had on the success of aspen regeneration 1 year after winter harvesting. Using high-resolution UAV imagery and maximum likelihood supervised image classification, residual slash was differentiated from the underlying forest floor. Overall, classification accuracy ranged between 85% and 96% with the highest accuracy occurring when aerial imagery was collected at the beginning of the second spring following winter harvesting. Slash distribution was quite consistent across harvested blocks, with 92% of harvested blocks experiencing <33% coverage. There was no relationship between the level of aspen regeneration following 1 year of growth and percentage slash coverage up to 60%. No vegetation plots occurred in areas with >60% slash coverage; therefore, it is unknown whether aspen regeneration will be affected in areas with higher slash coverage.

On Generalized Slash Distributions: Representation by Hypergeometric Functions

The popular concept of slash distribution is generalized by considering the quotient Z = X/Y of independent random variables X and Y, where X is any continuous random variable and Y has a general beta distribution. The density of Z can usually be expressed by means of generalized hypergeometric functions. We study the distribution of Z for various parent distributions of X and indicate a possible application in finance.