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CD4+CD8+ double positive (DP) precursors undergo positive selection in the thymus, and subsequently commit to either the CD4 or CD8 single positive (SP) lineage. Mice lacking Zap70, a crucial kinase involved in T-cell receptor (TCR) signal transduction are developmentally arrested at the DP stage, showing that this process depends on TCR signalling. Furthermore, the resultant SP populations are major histocompatibility (MHC) matched, as CD4 lineage cells recognise MHC-II whereas CD8 lineage T cells recognise MHC-I. There are currently two favoured models describing how the MHC restriction of the TCR correlates with lineage choice. These suggest that differences in either the TCR signalling strength or signalling length underlie the CD4/CD8 lineage decision during the DP stage. Both models posit that differences in signalling strength/length are properties that are conferred by the different signalling capacities of the CD4/CD8 coreceptors. However, questions remain over the mechanisms behind this process, including how the selecting cell interprets the proximal differences in TCR activation and whether the quality of this signal impacts on its future homeostatic survival potential. A major obstacle in addressing these questions is the lack of tools to facilitate understanding of the kinetic regulation of positive selection. We therefore sought to examine the kinetics of T-cell development using a tetracycline inducible Zap70 mouse model (TetZap70 hereon). In the absence of the tetracycline derivative doxycycline (dox), T-cells were arrested at the DP stage, prior to positive selection. However, the administration of dox induced positive selection of a synchronized wave of positively selecting thymocytes, enabling the resolution of intermediate populations of positively selecting DPs. We found that CD4 and CD8 lineage development occurred with temporal distinction, from phenotypically disparate populations of DP thymocytes. Furthermore, we found that endogenous Zap70 was developmentally regulated in different DP populations of WT mice, and loss of this regulation in TetZap70 mice corresponded to an impairment in CD8 lineage generation. Thus we suggest that temporal regulation of T-cell signalling sensitivity during thymic development facilitates the resolution of strong/consistent signals versus weak/intermittent signals. Finally we find evidence that the quality of the positive selection signal not only controls the CD4/CD8 lineage decision, but also impacts on the future homeostatic survival potential of T-cells by influencing levels of the prosurvival interleukin-7 receptor alpha chain (IL7rα).

This thesis is concerned principally with the problem of estimating the parameters of the Weibull and Beta distributions using several different techniques. These distributions are used in the area of reliability testing and it is important to achieve the best estimates possible of the parameters involved. After considering several accepted methods of estimating the relevant parameters, it is considered that the best method depends on the aim of the analysis, and on the value of the shape parameter β. For estimating the two-parameter Weibull distribution, it is recommended that Generalized Least Squares (GLS) is the best method to use for values of β between 0.5 and 30. However, Maximum Likelihood Estimator (MLE) is a good method for estimating quantiles. On this basis, the three-parameter Weibull distribution is investigated. The traditional parametrization is compared with a new parametrization developed in this work. By considering parameter effects and intrinsic curvature it is shown that the new parametrization results in a linear effect of the shape parameter. Also it has advantages in quantile estimation because of its ability to provide estimates for a wider range of data sets. A less frequently used distribution in the field of reliability is the Beta distribution. The lack of frequency of its use is partly due to the difficulty in estimating its parameters. A simple, applicable method is developed here of estimating these parameters. This 'group method' involves estimating the two ends of the distribution. It is shown that this procedure can be used, together with other methods of estimating the two- parameter Beta distribution successfully to estimate the four-parameter Beta distribution.

Estimation of the probability of occurrence of future flood events at one or more locations across a river system is frequently required for the design of bridges, culverts, spillways, dams and other engineering works. This study investigates some of the statistical aspects for estimating the flood frequency distribution at a single site and on regional basis. It is demonstrated that generalized logistic (GL) distribution has many properties well suited for the modelling of flood frequency data. The GL distribution performs better than the other commonly recommended flood frequency distributions in terms of several key properties. Specifically, it is capable of reproducing almost the same degree of skewness typically present in observed flood data. It appears to be more robust to the presence of extreme outliers in the upper tail of the distribution. It has a relatively simpler mathematical form. Thus all the well known methods of parameter estimation can be easily implemented. It is shown that the method of probability weighted moments (PWM) using the conventionally recommended plotting position substantially effects the estimation of the shape parameter of the generalized extreme value (GEV) distribution by relocating the annual maximum flood series. A location invariant plotting position is introduced to use in estimating, by the method of PWM, the parameters of the GEV and the GL distributions. Tests based on empirical distribution function (EDF) statistics are proposed to assess the goodness of fit of the flood frequency distributions. A modified EDF test is derived that gives greater emphasis to the upper tail of a distribution which is more important for flood frequency prediction. Significance points are derived for the GEV and GL distributions when the parameters are to be estimated from the sample data by the method of PWMs. The critical points are considerably smaller than for the case where the parameters of a distribution are assumed to be specified. Approximate formulae over the whole range of the distribution for these tests are also developed which can be used for regional assessment of GEV and GL models based on all the annual maximum series simultaneously in a hydrological region. In order to pool at-site flood data across a region into a single series for regional analysis, the effect of standardization by at-site mean on the estimation of the regional shape parameter of the GEV distribution is examined. Our simulation study based on various synthetic regions reveals that the standardization by the at-site mean underestimates the shape parameter of the GEV by about 30% of its true value and also contributes to the separation of skewness of observed and simulated floods. A two parameter standardization by the at-site estimates of location and scale parameters is proposed. It does not distort the shape of the flood frequency data in the pooling process. Therefore, it offers significantly improved estimate of the shape parameter, allows pooling data with heterogeneous coefficients of variation and helps to explain the separation of skewness effect. Regions on the basis of flood statistics L-CV and USKEW are derived for Scotland and North England. Only about 50% of the basins could be correctly identified as belonging to these regions by a set of seven catchment characteristics. The alternative approach of grouping basins solely on the basis of physical properties is preferable. Six physically homogeneous groups of basins are identified by WARD's multivariate clustering algorithm using the same seven characteristics. These regions have hydrological homogeneity in addition to their physical homogeneity. Dimensionless regional flood frequency curves are produced by fitting GEV and GL distributions for each region. The GEV regional growth curves imply a larger return period for a given magnitude flood. When floods are described by GL model the respective return periods are considerably smaller.

Transformation is a powerful tool for model building. In regression the response variable is transformed in order to achieve the usual assumptions of normality, constant variance and additivity of effects. Here the normality assumption is replaced by the Laplace distributional assumption, appropriate when more large errors occur than would be expected if the errors were normally distributed. The parametric model is enlarged to include a transformation parameter and a likelihood procedure is adopted for estimating this parameter simultaneously with other parameters of interest. Diagnostic methods are described for assessing the influence of individual observations on the choice of transformation. Examples are presented. In distribution methodology the independent responses are transformed in order that a distributional assumption is satisfied for the transformed data. Here the interest is in the family of distributions which are not dependent on an unknown shape parameter. The gamma distribution (known order), with special case the exponential distribution, is a member of this family. An information number approach is proposed for transforming a known distribution to the gamma distribution (known order). The approach provides an insight into the large-sample behaviour of the likelihood procedure considered by Draper and Guttman (1968) for investigating transformations of data which allow the transformed observations to follow a gamma distribution. The information number approach is illustrated for three examples end the improvement towards the gamma distribution introduced by transformation is measured numerically and graphically. A graphical procedure is proposed for the general case of investigating transformations of data which allow the transformed observations to follow a distribution dependent on unknown threshold and scale parameters. The procedure is extended to include model testing and estimation for any distribution which with the aid of a power transformation can be put in the simple form of a distribution that is not dependent on an unknown shape parameter. The procedure is based on a ratio, R(y), which is constructed from the power transformation. Also described is a ratio-based technique for estimating the threshold parameter in important parametric models, including the three-parameter Weibull and lognormal distributions. Ratio estimation for the weibull distribution is assessed and compared with the modified maximum likelihood estimation of Cohen and Whitten (1982) in terms of bias and root mean squared error, by means of a simulation study. The methods are illustrated with several examples and extend naturally to singly Type 1 and Type 2 censored data.