Semester 2

Date 
Presenter 
Title 
Abstract 
5 Aug 
Mr Muhammad Khan
The University of Newcastle

Transmuted families of lifetime distributions with mixture and covariates regression modelling to analyse survival data 
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[Supervisors: Dr. Robert King, Professor Irene Hudson, School of Mathematical and Physical Sciences]
Survival experiments are conducted in engineering and biomedical applications to evaluate the effect of a treatment on the distributions of lifetimes of people or things. In this research we introduce and study the transmuted families of lifetime distributions with applications of engineering, and biomedical sciences. This new class of distributions are obtained by using the quadratic rank transmuted map (QRTM) technique. We propose thirty six lifetime distributions. We also demonstrate a mixture and logtransmuted lifetime distributions for regression modelling of survival data. In this presentation we consider the transmuted generalized exponential (TGE) distribution, a mixture of TGE distributions and logTGE regression model from this family of lifetime distributions. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the quantile, moments, Beta, Shannon and Rényi entropies, mean deviation, Bonferroni and Lorenz curves, mean residual life and the rth moments of order statistics.
For the first time, we introduce mixture modelling for transmuted families of lifetime distributions. This research incorporates regression modelling to analyse survival data for the transmuted families of lifetime distributions. We also consider the log transmuted family of lifetime distributions for regression analysis of the relationship between a positivevalued dependent variable and one or more independent variables. The log TGE distribution is proposed and its moments derived. We also propose a log TGE regression model of a location and scale form, and discuss maximum likelihood estimation. Three applications with real data are given to illustrate the proposed distribution. The importance and flexibility of the TGE distribution is illustrated using bladder cancer data and also agitationsedation control data from ICU patients.

8 Aug 
Mr Jim Irish
The University of Newcastle

Statistical analyses of surname counts 
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[Supervisors: Dr. Robert King, Professor Irene Hudson, School of Mathematical and Physical Sciences]
Surname data have been investigated by several famous mathematicians, and there is no lack of stochastic models. However, tests of model predictions using the large data sets now available have not been undertaken with statistical rigour. Recent research has been undertaken mainly by physicists. Jim will describe the three aspects of his research:
 Selecting and validating appropriate models for the distribution of the number of surnames (in a sample or a population) with k namesakes
 Demonstrating that a ranksize distribution is inappropriate for modelling the surnames with the largest number of namesakes, and outlining a valid approach. (Ranksize distributions are widely used by nonstatisticians.) and
 Identifying methods to estimate the number of different surnames in a population based on counts from small random samples, and finding the sampling properties of the bestperforming estimators.
While Jim's work uses surname data from several populations, his work has applications to a much wider class of mathematical problems, which will be briefly noted.

5 Sep 
Dr Elizabeth Stojanovski
The University of Newcastle

Bayesian approach to Multivariate Methods 
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Concepts of health are often multivariate. Bayesian methods in the SEM framework are used to illustrate how different sources of uncertainty in data can be incorporated into the modelling process.

19 Sep 
Prof John Rayner
The University of Newcastle

Some Fresh Ideas in Elementary Nonparametrics 
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In Best et al. (2009) we looked at nonparametric tests in randomized block designs, with a particular focus on ties and ordered alternatives. Formulae were given for the Page, umbrella and Friedman test statistics. It was also noted that orthogonal trend contrasts can be used to partition the Friedman into the Page, umbrella and a residual.
In Thas et al. (2012) this work was extended to cover the completely randomized, randomized block and balanced incomplete block designs. Again there was an emphasis on ties and ordered alternatives and partitioning the KruskalWallis, Friedman and Durbin test statistics. The interpretation of these tests was also discussed. Without an assessment of the location shift (LS) model these tests cannot be interpreted in terms of location (mean/median) shift. The tests are consistent under the stochastic ordering model (SOM). Since SOM É LS conclusions other than location shift may be valid.
Recently we have extended an idea of Conover (1999) who, for randomized blocks and balanced incomplete blocks, suggested carrying out an analysis of variance (ANOVA) on the ranks and using the F test for treatment differences. Use of general linear model (GLM) routines permits the handling of ties and missing values. Empirical evidence demonstrates that the relevant F tests give test sizes generally at least as close to nominal as the competitor tests and power generally at least as good as that of the competitor tests.
References
BEST, D.J., RAYNER, J.C.W. and THAS, O. (2009). Nonparametric tests for randomized block data with ties and ordered alternatives. Proceedings of the Third Annual Applied Statistics Education and Research Collaboration (ASEARC) Research Conference, 78 December 2009: Newcastle, Australia.
CONOVER, W. (1999), Practical nonparametric statistics (3rd edn). New York: Wiley.
THAS, O., BEST, D.J. and RAYNER, J.C.W. (2012). Using orthogonal trend contrasts for testing ranked data with ordered alternatives. Statisticia Neerlandica, 66(4), 452471.
