Establishment Risks for Invasive Species

This article presents a quantitative methodology for evaluating the probability of invasive pest species establishing persistent populations. The estimation of pest establishment relies on data and information describing the biology and ecology of the pest and its interactions with potential host species and the regional environment. This information is developed using a model construct borrowed from theoretical population ecology. The methodology for estimating the probability of pest establishment is part of an overall framework that explores the implications of reductions in pest invasions on subsequent establishment. The risk reduction framework integrates the engineering aspects of different technologies for reducing pest entry, the biology and ecology of pest species, the suitability of potentially susceptible hosts, and the quality of available habitats. The methodology for estimating the risk of establishment is presented using an example pest, the Asian longhorned beetle ( Anoplophora glabripennis ), which has been introduced into the United States via solid wood packing materials (SWPM) used in international commerce. Uncertainties inherent to the estimation of model parameters that determine the risk of establishment are defined, quantified, and propagated through the population model. Advantages and limitations of the proposed methodology are discussed along with recommendations to make the approach more useful in the management of risks posed by the establishment of pest populations.     

Distribution of extremes of<Emphasis Type="Italic">r</Emphasis><Superscript>th</Superscript> concomitant from the Morgenstern family

In the present paper the distribution theory of maximum and minimum of ther ^th concomitants from k independent subgroups each of same size m from the Morgenstern family is investigated. Some applications of the results in estimation of the scale parameter of a marginal variable in the bivariate uniform distribution and a selection problem are discussed.     

Nonparametric Estimation of the Geometric Vitality Function

Recently, Nair and Rajesh (2000 Nair , K. R. M. , Rajesh , G. ( 2000 ). Geometric vitality function and its application to reliability . IAPQR Tran. 25 ( 1 ): 1 – 8 . [Google Scholar]) proposed a measure to describe the failure pattern of components/devices in terms of the geometric mean of the residual life. This measure find applications in modeling life time data. In the present work we provide a nonparametric kernel-type estimator for the geometric vitality function, both in the case of complete and censored samples. The properties of the estimator, under certain regularity conditions, are studied. The performance of the estimator is compared with the empirical estimator using a real data set and simulation studies are carried out using the Monte Carlo method.     

A Class of Distributions with Linear Hazard Quantile Function

In this article, we introduce and study a class of distributions that has linear hazard quantile function. Various distributional properties and reliability characteristics of the class are studied. Some characterizations of the class of distributions are presented. The method of L-moments is employed to estimate parameters of the class of distributions. Finally, we apply the proposed class to a real data set.