Moments of a product Pearson type VII density distribution

A new Pearson type VII distribution is introduced by taking the product of two Pearson type VII pdfs. Detailed moment properties and particular cases are derived.     

Modelling the spread in space and time of an airborne plant disease

Summary.  A spatiotemporal model is developed to analyse epidemics of airborne plant diseases which are spread by spores. The observations consist of measurements of the severity of disease at different times, different locations in the horizontal plane and different heights in the vegetal cover. The model describes the joint distribution of the occurrence and the severity of the disease. The three-dimensional dispersal of spores is modelled by combining a horizontal and a vertical dispersal function. Maximum likelihood combined with a parametric bootstrap is suggested to estimate the model parameters and the uncertainty that is attached to them. The spatiotemporal model is used to analyse a yellow rust epidemic in a wheatfield. In the analysis we pay particular attention to the selection and the estimation of the dispersal functions.     

The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs

The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and the red edges have a given fixed cost, representing the competitor’s prices. The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. We study this problem in the cases of planar and bounded-treewidth graphs. We show that the problem is NP-hard on planar graphs but can be solved in polynomial time on graphs of bounded treewidth.     

E- and R-optimality of block designs for treatment-control comparisons

Abstract

We study optimal block designs for comparing a set of test treatments with a control treatment. We provide the class of all E-optimal approximate block designs, which is characterized by simple linear constraints. Based on this characterization, we obtain a class of E-optimal exact designs for unequal block sizes. In the studied model, we provide a statistical interpretation for wide classes of E-optimal designs. Moreover, we show that all approximate A-optimal designs and a large class of A-optimal exact designs for treatment-control comparisons are also R-optimal. This reinforces the observation that A-optimal designs perform well even for rectangular confidence regions.     

Inspection errors in link sampling

Results of an investigation into the sensitivity to two types of inspection error of link sampling procedures described by Harischchandra and Srivenkataramana are reported. Relevant compound distributions are derived. Some comparisons with results obtained in a similar investigation for standard double sampling are also given.     

Dorfman-sterrett screening (group testing) schemes and the effects of faulty inspection

The Dorfman screening procedure is based on first testing a group of items as a whole, proceeding to individual testing only if the group-test indicates existence of at least one nonconforming item. A modification suggested by Sterrett allows for reintroduct-ion of group testing of all items, not yet tested individually, when an item is classified as nonconforming by an individual test. Effects of faulty test inspection on the properties of the modified procedures are studied.