Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1976. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 166-172).

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 190-199).

D.Phil. / We consider two problems relating to location-scale families of distributions. Firstly, we consider methods of parameter estimation when two samples come from the same type of distribution, but possibly differ in terms of location and spread. Although there are methods of estimation that are asymptotically efficient, our interest is in fi…nding methods which also have good small-sample properties. Secondly, we consider tests for the hypothesis that two samples come from the same location-scale family. Both these problems are addressed using methods based on empirical distribution functions and empirical characteristic functions.

Orientador: Laura Leticia Ramos Rifo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T15:05:12Z (GMT). No. of bitstreams: 1 Tasca_GustavoHenrique_M.pdf: 979052 bytes, checksum: bb1371bb1b8626882cebcf01550bb823 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho, estudamos métodos de inferência bayesiana para distribuições de cauda longa, que não envolvam o cálculo da função de verossimilhança. Inicialmente, apresentamos uma análise das propriedades de distribuições de cauda pesada e seus casos particulares, como as famílias de distribuições de cauda longa, subexponenciais e de variação regular. Apresentamos algumas estatísticas e seus comportamentos amostrais, a fim de desenvolvermos medidas de diagnóstico. Para obtenção de inferências a posteriori, discutimos o método ABC de mínima entropia e outros algoritmos para verificação e seleção de modelos, que não utilizam o cálculo da função de verossimilhança. Introduzimos um novo algoritmo para seleção de modelos baseado na distribuição preditiva a posteriori, cujos resultados são validados através de simulações e análises de dados reais relacionados à hidrologia / Abstract: In this work, we study Bayesian inference methods for long-tailed distributions that don't involve the evaluation of the likelihood function. Initially, we present an analysis of the properties of heavy-tailed distributions and particular cases, as long-tailed, subexponencial and regular variation families. Some statistics are presented and their sampling behavior studied, in order to develop diagnostic measures. For obtaining posterior inferences, we discuss the minimum entropy ABC and others likelihood-free algorithms, aiming model checking and model selection. We introduce a new model selection algorithm based on the posterior predictive distribution, the results of which are validated through simulations and real data related to river flow / Mestrado / Estatistica / Mestre em Estatística

Dissertation submitted for Masters of Science degree in Mathematical Statistics in the FacultyofScience, SchoolofStatisticsandActuarialScience, University of the Witwatersrand Johannesburg, January 2018 / This dissertation focuses on demonstrating the use of extreme value theory in modelling temperature in South Africa. The purpose of modelling temperature is to investigate the frequency of occurrences of extremely low and extremely high temperatures and how they influence the demand of electricity over time. The data comprise a time series of average hourly temperatures that are collected by the South African Weather Service over the period 2000−2010 and supplied by Eskom. The generalized extreme value distribution (GEVD) for r largest order statistics is fitted to the average maximum daily temperature (non-winter season) using the maximum likelihood estimation method and used to estimate extreme high temperatures which result in high demand of electricity due to use of cooling systems. The estimation of the shape parameter reveals evidence that the Weibull family of distributions is an appropriate fit to the data. A frequency analysis of extreme temperatures is carried out and the results show that most of the extreme temperatures are experienced during the months January, February, November and December of each year. The generalized Pareto distribution (GPD) is firstly used for modelling the average minimum daily temperatures for the period January 2000 to August 2010. A penalized regression cubic smoothing spline is used as a time varying threshold. We then extract excessesabovethecubicregressionsmoothingsplineandfitanon-parametricmixturemodel to get a sufficiently high threshold. The data exhibit evidence of short-range dependence and high seasonality which lead to the declustering of the excesses above the threshold and fit the GPD to cluster maxima. The estimate of the shape parameter shows that the Weibullfamilyofdistributionsisappropriateinmodellingtheuppertailofthedistribution. The stationary GPD and the piecewise linear regression models are used in modelling the influence of temperature above the reference point of 22◦C on the demand of electricity. The stationary and non-stationary point process models are fitted and used in determining the frequency of occurrence of extremely high temperatures. The orthogonal and the reparameterizationapproachesofdeterminingthefrequencyandintensityofextremeshave i been used to establish that, extremely hot days occur in frequencies of 21 and 16 days per annum, respectively. For the fact that temperature is established as a major driver of electricity demand, this dissertation is relevant to the system operators, planners and decision makers in Eskom and most of the utility and engineering companies. Our results are furtherusefultoEskomsinceitisduringthenon-winterperiodthattheyplanformaintenance of their power plants. Modelling temperature is important for the South African economy since electricity sector is considered as one of the most weather sensitive sectors of the economy. Over and above, the modelling approaches that are presented in this dissertation are relevant for modelling heat waves which impose several impacts on energy, economy and health of our citizens. / XL2018

No description available.

Approximate formulae are derived for obtaining confidence intervals for the probabilities of a multinomial distribution. The approach used is to consider the Chi-square goodness of fit statistic as a function of the population parameters and to invert this function to obtain a set of simultaneous confidence intervals for the parameters The confidence coefficient for the set of simultaneous confidence intervals obtained by this procedure is conservative, i.e., the true probability that every interval covers its corresponding parameter will in general be greater than the coefficient obtained by this method. As the sample size increases the intervals will converge on the population parameters and will estimate them exactly in the limit. / Master of Science

The use of availability measures is very informative when analyzing the performance of repairable components. The derivation and evaluation of such measures is usually focused on describing the status of the component over time. It is not generally acknowledged that the resulting availability measure is in fact an expected value with respect to frequency. In a population of n independent, identical components, the number functioning at any point in time is a random variable. The distribution of this random variable is determined and described here. The intuitive view that this frequency distribution is binomial is verified. This is accomplished using direct analysis and Monte Carlo simulation. Two general cases are considered: (1) components with exponential life and repair time distributions, and (2) components with Weibull life distributions and exponential repair time distributions. The analysis leads to more accurate models of component behavior in terms of frequency including an exact confidence bound on the number of components functioning at any point in time. In addition, the time evolution of the frequency distribution is described and the relationships between the frequency distribution and the life and repair time distribution parameters are explored. Finally, the implications for availability decision analyses are shown. The overall result is a new perspective on availability which should prove to be very useful. / Master of Science

This paper proposed the idea that the growth of an individual organism follows a mathematical model very closely and that different individuals follow different members of the same parametric family of models. This idea implies that the variation observed between individuals measured at the same time arises not from an additive term as has been previously supposed, but primarily from variation of the parameters of the model. A graph of data from an experiment on chickens is included which points up this individuality and the increased variation resulting from the passage of time. The four models considered were growth curves employing two, three, and four parameters with biological interpretations existing for the parameters. The parameters were allowed to follow independent uniform distributions and independent gamma distributions. / Master of Science