Robustness of tests for directional mean

In this paper we study the robustness of the likelihood ratio, circular mean and circular trimmed mean test functionals in the context of tests of hypotheses regarding the mean direction of circular normal and wrapped normal distributions. We compute the level and power breakdown properties of the three test functionals and compare them. We find that the circular trimmed mean test functional has the best robustness properties for both the above-mentioned distributions. The level and power properties of the test statistics corresponding to these functionals are also studied. Two examples with real data are given for illustration. We also consider the problem of testing the mean direction of the von-Mises–Fisher distribution on the unit sphere and explore the robustness properties of the spherical mean direction and likelihood ratio test functionals.     

Estimating parameters of a selected Pareto population

Let Π₁,…,Π_k be k populations with Π_i being Pareto with unknown scale parameter α_i and known shape parameter β_i;i=1,…,k. Suppose independent random samples (X_i1,…,X_in), i=1,…,k of equal size are drawn from each of k populations and let X_i denote the smallest observation of the ith sample. The population corresponding to the largest X_i is selected. We consider the problem of estimating the scale parameter of the selected population and obtain the uniformly minimum variance unbiased estimator (UMVUE) when the shape parameters are assumed to be equal. An admissible class of linear estimators is derived. Further, a general inadmissibility result for the scale equivariant estimators is proved.     

Habitat-wise distribution of the House Sparrow (<Emphasis Type="Italic">Passer domesticus</Emphasis>) in Delhi,India

Recently, there have been several reports from different parts of the World on the declining populations of the House Sparrow (Passer domesticus). In order to assess the population of this species in the National Capital Territory of Delhi-India, this study was conducted during June– August in 2007. Twenty-eight Fixed-Radius Point Count stations were established in five habitat types viz. High-density Urban Area, Medium-density Urban Area, Low-density Urban Area, Agriculture Area, and Forested Area, within the study area. The results show that the House Sparrow is still a dominant species in the agriculture area. However, its density is very low in the urban areas as compared to the other co-occurring common bird species viz. Rock Pigeon (Columba livia domestica), House Crow (Corvus splendens) and Common Myna (Acridotheres tristis). As, this study was conducted only over one season, the data is not sufficient to provide a clear picture of the population trend of the House Sparrow. Further studies are therefore required to investigate the relationship of the House Sparrow with other co-occurring common species, and to analyse the data on the type and quality of greenspaces and their relation with the House Sparrow in the study area. A long-term monitoring and conservation programme involving local people may be a good approach for maintaining the population of House Sparrow in the study area.     

Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring

We consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtub-shaped distribution on the basis of progressive type-II censored sample. The maximum likelihood estimators and Bayes estimators are derived for two unknown parameters, reliability function and hazard function. The Bayes estimators are obtained against squared error, LINEX and entropy loss functions. Also, using the Lindley approximation method we have obtained approximate Bayes estimators against these loss functions. Some numerical comparisons are made among various proposed estimators in terms of their mean square error values and some specific recommendations are given. Finally, two data sets are analyzed to illustrate the proposed methods.     

Choosing a diversification project in a regulated economy

Choosing a diversification project in a regulated economy involves consideration of a large number of micro and macro issues. In order to make an optimal choice of strategy, a formal approach to diversification planning is necessary. This article develops an approach which aims at breaking up the problem of identification and selection of projects into manageable components. The approach involves three steps: identification of broad industry groups: identification of specific projects within each broad industry group; and comprehensive feasibility study. The major benefit of this approach lies in providing a systematic mechanism for reducing the number of alternatives and in recognizing the link between the internal management processes of strategy formulation with the political and administrative processes in government and regulatory bodies. The article is based largely on the Indian experience.     

On the relation between Wiener index and eccentricity of a graph

Journal of Combinatorial Optimization - The relation between the Wiener index W(G) and the eccentricity $$\varepsilon (G)$$ of a graph G is studied. Lower and upper bounds on W(G) in terms of...     

SB-robustness of directional mean for circular distributions

In this paper we study the robustness of the directional mean (a.k.a. circular mean) for different families of circular distributions. We show that the directional mean is robust in the sense of finite standardized gross error sensitivity (SB-robust) for the following families: (1) mixture of two circular normal distributions, (2) mixture of wrapped normal and circular normal distributions and (3) mixture of two wrapped normal distributions. We also show that the directional mean is not SB-robust for the family of all circular normal distributions with varying concentration parameter. We define the circular trimmed mean and prove that it is SB-robust for this family. In general the property of SB-robustness of an estimator at a family of probability distributions is dependent on the choice of the dispersion measure. We introduce the concept of equivalent dispersion measures and prove that if an estimator is SB-robust for one dispersion measure then it is SB-robust for all equivalent dispersion measures. Three different dispersion measures for circular distributions are considered and their equivalence studied.