Showing papers by "Barry C. Arnold published in 2006"

Families of Multivariate Distributions Involving the Rosenblatt Construction

Abstract: Recently, Jones pointed out a useful device for enriching families of univariate distributions. Typically, one may construct a random variable with distribution F by considering F−1(U),where U is a uniform (0,1) random variable. Jones suggested replacing the uniform random variable by a beta-distributed random variable. In this article an analogous enriching process is applied to the Rosenblatt construction of multivariate distributions. Several parametric families are introduced using this construction, together with discussion of appropriate parameter estimation strategies. It turns out that the resulting families of distributions are very flexible and easy to estimate. The method is illustrated with simulated and real data.

Recent advances in the analyses of directional data in ecological and environmental sciences

Abstract: Directional data (DD) generally refer to data on angular propagations or displacements, orientations, directional movements, etc. Periodic data, such as those recorded on hour of the day, day of the week, etc. can be viewed as and are also cast in the arena of DD through transformations to representative angles. The DD are encountered in all areas of applied sciences, presumably more prominently in ecological and environmental sciences (EES). Research on paleoenvironment often necessitates the hind-casting of directions of river flows obtained from the azimuthal direction of the current that formed the crossbeds. Significance of multimodality of cross-bedding orientations suggests multiple paleoperiods corresponding to varying transport conditions. Orientations of poles to beddings constitute three-dimensional directional data. Directions of remnant magnetism on rock cores are important data in paleontology and earth sciences, e.g. as in the study of reversal of polarity of earth. Studies on the directional movements of ice-floes and ice-bergs are indispensable for planning of transport and of routing of ocean-liners on the confused seas and oceans. Variations in the flight directions of migratory birds form the basis of the evolution of new migratory routes. Displacements in the wintering trajectory of migratory species in search of new breeding areas for colonisation or in their subsequent homing directions are important predictors of environmental and ecological changes. Such a change is often attributed to microevolutionary processes and also to possibly a selection from the earlier used list of genetically based migratory directions. These also lead to changes in the size of the wintering population as well as suggest the mode of the way of inheritance. Corresponding directional measurements may be obtained from ring recoveries, cage experiments or satellite-based radio telemetry. Peak directions of dissolved oxygen, pH value, algae concentration,

Probability distributions and statistical inference for axial data

Abstract: Observations on axes which lack information on the direction of propagation are referred to as axial data Such data are often encountered in enviromental sciences, eg observations on propagations of cracks or on faults in mining walls Even though such observations are recorded as angles, circular probability models are inappropriate for such data since the constraint that observations lie only in [0, π) needs to be enforced Probability models for such axial data are argued here to have a general structure stemming from that of wrapping a circular distribution on a semi-circle In particular, we consider the most popular circular model, the von Mises or circular normal distribution, and derive the corresponding axial normal distribution Certain properties of this distribution are established Maximum likelihood estimation of its parameters are shown to be surprisingly, in contrast to trigonometric moment estimation, numerically quite appealing Finally we illustrate our results by several real life axial data sets