Comparison between the rates of convergence of extremes under linear and under power normalization

By using the theory of the second-order regular variation, we study the rates of the weak convergence of the maximum order statistics under power normalization. The exact rates are obtained in the uniform metric and the total variation metric. The relationship between the rates of convergence under linear and under power normalization is derived. Some illustrative examples are given for comparing the rates of convergence.     

Bayesian prediction bounds for the pareto lifetime model

Suppose that the length of time in years for which a business operates until failure has a Pareto distribution. Let x₁ ≤ x₂ x₃ ≤…≤z_k denote the survival lifetimes of the first k of a random sample of n businesses. Bayesian predictions are to be made on the ordered failure times of t h e remaining (n-k) businesses, using the conditional probability density function. Examples are given to illustrate our results.     

Bayesian prediction based on finite mixtures of lomax components model and type i censoring

This paper is concerned with the problem of obtaining Bayesian prediction bounds for future observations based on a type I censored sample from a nonhomogerieous population having a distribution which is a mixture of two Lomax components. A numerical example is given to illustrate our results.     

Bayesian prediction with a random sample size for the burr lifetime distribution

This paper is concerned with the problem of deriving Bayesian prediction bounds for the Burr distribution when the sample size is a random variable. Prediction bounds for both the future observations (the case of two-sample prediction) and the remaining observations in the same sample (the case of one-sample prediction) will be derived. The analysis will depend mainly on assuming that the size of the sample is a random variable having the Poisson distribution. Finally, numerical examples are given to illustrate the results.     

Bayesian prediction for two-parameter weibull lifetime models

Prediction methods for the two-parameter Weibull distribution are computationally complicated. This paper shows how an approximate Bayesian method can be used to simplify the computation and presents a simpler alternative for computing prediction bounds derived classically by Lawless (1973).     

New directions for management accounting

Using a general systems rationale, this paper develops a theoretical structure for approaching the problem of management accounting. The management control problem is explicated in terms of maintaining a relationship between the enterprise's structure and its environment. An enterprise's structure is composed of three elements (and their inter-relations): a decision and control subsystem; a financial funds subsystem and an operating (physical transforms) subsystem. Portrayed in these terms, the problem of management accounting is shown to require a methodology which is able to take cognizance of economic, sociological, psychological and other aspects of the enterprise system. The model described here provides a general intellectual frame of reference for ordering the problem.     

Limit theorems for random maximum of independent and non-identically distributed random vectors

In this paper, we study the weak convergence of the random maximum of independent and non-identical random vectors. When the random sample size is assumed to be independent of the basic variables and its distribution function is assumed to converge weakly to a non-degenerate limit, the necessary and sufficient conditions for the weak convergence of the random maximum are derived. An illustrative example is given.     

The estimations under power normalization for the tail index,with comparison

It is well known that the max-stable laws under power normalization attract more distributions than that under linear normalization. This fact practically means that the classical linear model (L-model) may fail to fit the given extreme data, while the power model (P-model) succeeds to do that. The main object of this paper is developing the modeling of extreme values via P-model by suggesting a simple technique to obtain a parallel estimator of the extreme value index (EVI) in the P-model for every known estimator to the corresponding parameter in L-mode. An application of this technique yields two classes of moment and moment ratio estimators for EVI in the P-model. The performances of these estimators are assessed via a simulation study. Moreover, an efficient criterion for comparing the L and P models is proposed to choose the best model when the two models successfully work.     

Limit distributions of order statistics with random indices in a stationary Gaussian sequence

In this article, we study the limit distributions of the extreme, intermediate, and central order statistics (os) of a stationary Gaussian sequence under equi-correlated setup. When the random sample size is assumed to converge weakly and to be independent of the basic variables, the sufficient (and in some cases the necessary) conditions for the convergence are derived. Finally, we show that the obtained result for the maximum os, with random sample size, is also applicable in the case of the non constant correlation case.     

Researching social care for minority ethnic older people: implications of some Scottish research

Summary The paper explores issues raised by research on patterns ofwelfare and mutual care among older Pakistani people and theirfamilies, with particular reference to their use, or lack ofuse of social care services. Qualitative interviews were conductedwith (self-defined) minority ethnic older people, professionalsin statutory services and in minority-led community-based groups.The organization of services is discussed, with special referenceto issues of power and control, the role of the voluntary (non-profit)and statutory sectors, the debate regarding the possible needfor specialist versus generic services, and the role of minority-ledinitiatives. Secondly, issues of service staffing are examined,and the dangers of marginalizing minority services and staffreviewed, especially with reference to divisions of labour inservice provision and staff's own perspectives. Thirdly, themethodological implications of the work are explores, includingissues of linguistic and cultural communication and workingwith relatively powerless social groups, whose views are sought.Examining the views of professional social care workers is alsoproblematized, with reference to their gate-keeping role. Itis argued that user perspectives are essential to the developmentof appropriate services for minority ethnic groups. In conclusion,the need to raise these issues in other work is discussed.