No description available.

No description available.

No description available.

This thesis addresses a diverse range of topics in the area of probabilistic seismic risk analysis of engineering facilities. This intentional path of diversity has been followed primarily because of the relatively new and rapid development of this facet of earthquake engineering. As such this thesis focuses on the rigorous scrutinization of current, and in particular, simplified methods of seismic risk assessment; the development of novel aspects of a risk assessment methodology which provides easily communicated performance measures and explicit consideration for the many uncertainties in the entire earthquake problem; and the application of this methodology to case-study examples including structures supported on pile foundations embedded in liquefiable soils. The state-of-the-art in seismic risk and loss assessment is discussed via the case study of a 10 storey New Zealand office building. Particular attention is given to the quality and quantity of information that such assessment methodologies provide to engineers and stakeholders for rational decision-making. Two chapters are devoted to the investigation of the power-law model for representing the ground motion hazard. Based on the inaccuracy of the power-law model at representing the seismic hazard over a wide range of exceedance rates, an alternative, more accurate, parametric hazard model based on a hyperbola in log-log space is developed and applied to New Zealand peak ground acceleration and spectral acceleration hazard data. A semianalytical closed-form solution for the demand hazard is also developed using the hyperbolic hazard model and applied for a case-study performance assessment. The power-law hazard model is also commonly used to obtain a closed-form solution for the annual rate of structural collapse (collapse hazard). The magnitude of the error in this closed-form solution due to errors in the necessary functional forms of its constitutive relations is examined via a parametric study. A series of seven chapters are devoted to the further development of various aspects of a seismic risk assessment methodology. Intensity measures for use in the estimation of spatially distributed seismic demands and seismic risk assessment which are: easily predicted; can predict seismic response with little uncertainty; and are unbiased regarding additional properties of the input ground motions are examined. An efficient numerical integration algorithm which is specifically tailored for the solution of the governing risk assessment equations is developed and compared against other common methods of numerical integration. The efficacy of approximate uncertainty propagation in seismic risk assessment using the so-called First-Order Second-Moment method is investigated. Particular attention is given to the locations at which the approximate uncertainty propagation is used, the possible errors for various computed seismic risk measures, and the reductions in computational demands. Component correlations have to date been not rigorously considered in seismic loss assessments due to complications in their estimation and tractable methodologies to account for them. Rigorous and computationally efficient algorithms to account for component correlations are presented. Particular attention is also given to the determination of correlations in the case of limited empirical data, and the errors which may occur in seismic loss assessment computations neglecting proper treatment of correlations are examined. Trends in magnitude, distribution, and correlation of epistemic uncertainties in seismic hazard analyses for sites in the San Francisco bay area are examined. The characteristics of these epistemic uncertainties are then used to compare and contrast three methods which can be used to propagate such uncertainties to other seismic risk measures. Causes of epistemic uncertainties in component fragility functions, their evaluation, and combination are also examined. A series of three chapters address details regarding the seismic risk assessment of structures supported on pile foundations embedded in liquefiable soils. A ground motion prediction equation for spectrum intensity (found to be a desirable intensity measure for seismic response analysis in liquefiable soils) is developed based on ground motion prediction equations for spectral accelerations, which are available in abundance in literature. Determination of intensity measures for the seismic response of pile foundations, which are invariably located in soil deposits susceptible to liquefaction, is examined. Finally, a rigorous seismic performance and loss assessment of a case-study bridge structure is examined using rigorous ground motion selection, seismic effective stress analyses, and professional cost estimates. Both direct repair and loss of functionality consequences for the bridge structure are examined.

No description available.

Skewness and elongation are two factors that directly determine the shape of a probability distribution. Thus, to obtain a flexible distribution it is always desirable that the parameters of the distribution directly determine the skewness and elongation. To meet this purpose, Tukey (1977) introduced a family of distributions called g-and-h family (gh family) based on a transformation of the standard normal variable where g and h determine the skewness and the elongation, respectively. The gh family of distributions was extensively studied by Hoaglin (1985) and Martinez and Iglewicz (1984). For its flexibility in shape He and Raghunathan (2006) have used this distribution for multiple imputations. Because of the complex nature of this family of distributions, it is not possible to have an explicit mathematical form of the density function and the estimates of the parameters g and h fully depend on extensive numerical computations.In this study, we have developed algorithms to numerically compute the density functions. We present algorithms to obtain the estimates of g and h using method of moments, quantile method and maximum likelihood method. We analyze the performance of each method and compare them using simulation technique. Finally, we study some special cases of gh family and their properties. / Department of Mathematical Sciences

There is no abstract available for this thesis.

The family of univariate skew-normal probability distributions, an extension of symmetric normal distribution to a general case of asymmetry, was originally proposed by Azzalani [1]. Since its introduction, very limited research has been conducted in this area. An extension of the univariate skew-normal distribution to the multivariate case was considered by Azzalani and Dalla Valle [4]. Its application in statistics was recently considered by Azzalani and Capitanio [3]. As a general result, Azzalani (1985) [See [1]] showed that, any symmetric distribution can be viewed as a member of a more general class of skewed distributions.In this study we establish some properties of general family of skewed distributions. Examples of general family of asymmetric distributions is presented in a way to show their differences from the corresponding symmetric distributions. The skew-logistic distribution and its properties are considered in great details. / Department of Mathematical Sciences

No description available.

ix, 147 leaves / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.) from the Dept. of Statistics, University of Adelaide, 1971