Trevor F. Cox

Optimising the queuing system for an ear, nose and throat outpatient clinic

Several authors have considered the problem of the efficient running of hospital outpatient clinics. The first solution was probably by Welch & Bailey (1952). More recent authors include Fetter & Thompson (1966), Vissers (1979), Stafford & Aggarwal (1979). The Ear, Nose and Throat outpatient clinic presents a special case due to the complex queuing structure involved, which is described in the next section. A simulation of this special clinic was undertaken, any useful theoretical results being impossible to obtain.

Multidimensional scaling on a sphere

Nonmetric multidimensional scaling (MDS) is adapted to give configurations of points that lie on the surface of a sphere.There are data sets where it can be argued that spherical MDS is more relevant than the usual planar MDS.The theory behind the adaption of planar MDS to spherical MDS is outlined and then its use is illustrated on three data sets.

A General Weighted Two-Way Dissimilarity Coefficient

Choosing dissimilarity/similarity (proximity) measures for mixed data is not always easy. Gower (1971) has suggested a measure which has become popular in practical applications. This paper suggests an extension to his measure for calculating pairwise dissimilarities for individuals (objects) which also simultaneously produces a set for the variables. The definition of the dissimilarities incorporates the automatic weighting of individuals and variables. The dissimilarities can be used for multidimensional scaling or other statistical techniques that use proximities for both the individuals and variables, with the weights providing information on the relative contribution of each individual and variable in the analysis. The new method is tested by a simulation exercise and then used successfully on three empirical data sets.

Interpreting stress in multidimensional scaling

Several authors have studied the stress associated with a configuration of points obtained from non-metric multidimensional scaling. Most studies involve the simulation of a configuration of points in a Euclidean space from which dissimilarities are derived usually in the form of distances between points together with associated errors. The dissimilarities are then used to attempt to recover the initial configuration of points using multidimensional scaling. The resulting stress for the configuration is then related to dimension of the space, parameters of the associated errors, etc. This paper uses similar methods to these previous ones but by introducing uniform errors instead of the usual normal errors interesting results occur. It is found that a linear relationship occurs between stress and the parameter of the uniform errors and indeed this linear relationship is approximately invariant to the number of points in the configuration and to the spatial pattern of the configuration. This leads directly ...

On the design of efficient experiments for choosing between two bernoulli populations

An experiment consists of taking samples one at a time from two Bernoulli populations. At the conclusion of the experiment one of the two populations is declared to have the higher probability of sucess.We propose two classes rules for sampling and for choosing a population which results which results good decisions made quickly.These rules are analysed and are compared suggested previously by means of Monte-Carlo simulations.

Nearest Neighbours to Nearest Neighbours

The distribution of the distance from an arbitrary point to the nth nearest event within a two-dimensional Poisson process is well known and appears frequently in the literature. These and other nearest neighbour distances have often been used for analyses of two-dimensional Poisson processes and other spatial patterns; such analyses may include testing for randomness and the robust estimation of density. In this article nearest neighbour distances are not considered but the related problem of nearest neighbours to nearest neighbours. The probability is found that the mtth nearest neighbour to an arbitrary point within a two-dimensional Poisson process is the kth nearest neighbour to the nth nearest neighbour of the original point. Similar nearest neighbour relationships are also considered. Two possible users are outlined for results obtained.

The generalized likelihood ratio test for the Behrens–Fisher problem

A solution is suggested for the Behrens-Fisher problem of testing the equality of the means from two normal populations where variances are unknown and not assumed equal, by considering an adaption of the generalized likelihood ratio test. The test developed and called the adjusted likelihood ratio test has size close to the nominal significance level and compares favourably with regard to size and power to the Welch-Aspin test. An asymptotic result shows the connection between the generalized likelihood ratio test and the most commonly used test statistic for the Behrens-Fisher problem.

The maximum non-unit eigenvalue for the Wright-Fisher model of random genetic drift incorporating selection

Abstract The largest non-unit eigenvalue λ of the transition matrix for the Wright-Fisher Markov chain model of random genetic drift is found numerically with selective advantages of genotypes taken into account. Polynomials in the selection coefficients are fitted to λ in order to summarize the behaviour of λ with varying selection. Also found are the values of the selective advantages which give rise to an acceleration to the rate of fixation of alleles. These values are compared to results for the diffusion approximation to the Wright-Fisher model.