Submitted by Guilherme Aparecido Santos Aguilar null (guiaguilar@hotmail.com) on 2017-03-24T20:21:32Z No. of bitstreams: 1 dissertacao.pdf: 1514798 bytes, checksum: 2336853543dbc4bd478bff182d7bc837 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-03-27T17:03:00Z (GMT) No. of bitstreams: 1 aguilar_gas_me_prud.pdf: 1514798 bytes, checksum: 2336853543dbc4bd478bff182d7bc837 (MD5) / Made available in DSpace on 2017-03-27T17:03:00Z (GMT). No. of bitstreams: 1 aguilar_gas_me_prud.pdf: 1514798 bytes, checksum: 2336853543dbc4bd478bff182d7bc837 (MD5) Previous issue date: 2017-03-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Devido aos inúmeros campos para aplicações na Análise de Sobrevivência, diferentes funções de risco são necessárias para modelar os mais diversos casos em estudo. Portanto, ao criar novas distribuições pode-se obter diferentes funções de risco com suas diferentes curvas, que podem ser utilizadas para diversos tipos de dados. Serão apresentadas três novas distribuições de probabilidade, criadas a partir de três diferentes métodos, sendo a Gama Exponenciada Estendida de Marshall Olkin, Gama Exponenciada Poisson Truncada no Zero e também a Gama Exponenciada Bivariada. Para as distribuições de probabilidade univariadas foram obtidos resultados probabilísticos, tais como o n-ésimo momento; r-ésimo momento de vida média residual; r-ésimo momento de vida média residual invertido; ordenação estocástica; entropias; desvios médios; curvas de Bonferroni e de Lorenz; assimetria, curtose e seus gráficos; estatísticas de ordem e parâmetro stress − strength. Em relação a distribuição Gama Exponenciada Bivariada foi encontrada sua função acumulada; função densidade; função marginal; função condicional e seu n-ésimo momento. Para as novas distribuições univariadas encontradas, também foram feitas simulações para diferentes valores de parâmetros com o intuito de verificar qual o melhor método de estimação, para cada parâmetro de cada distribuição. Os métodos utilizados foram: estimador de máxima verossimilhança, Mínimos Quadrados, Mínimos Quadrados Ponderados, Cramér-von-Mises, Anderson Darling, Anderson Darling -RT (cauda à direita), Anderson Darling - LT (cauda à esquerda), Anderson Darling - 2LT (cauda à esquerda de segunda ordem), Kolmogorov e também foi utilizado o método Bayesiano com priori Gama. Por último foram também realizadas aplicações em um banco de dados, uma para cada distribuição univariada, onde foi comparado o ajuste das novas distribuições propostas com outras já conhecidas na literatura. / Due to the many fields for applications in Survival Analysis, different hazard functions are needed to modelling the various case studies. Therefore, creating new distributions can obtains different hazard functions with different graphics, which can be used for various types of data. There will be presented three new probability distributions, created from three different methods, the Marshall Olkin Extendet Exponentiated Gamma, Poisson Zero Truncated Exponentiated Gamma and the Bivariate Exponentiated Gamma. For such univariate probability distributions it will be obtained some probabilistics results, like n-th time, rth moment of residual life, r-th moment of residual life inverted, stochastic ordering, entropies, mean deviation, Bonferroni and Lorenz curve, skewness, kurtosis, order statistics and stress-strength parameter. Regarding the Bivariate Gamma Exponentiated was found your acumulated and density function; marginal function; conditional function and it’s n-th moment. For the new univariate distributions found, were also made simulations for different parameter values in order to find the best estimation method for each parameter. The methods used were: maximum likelihood, ordinary least-squares, weighted least-squares, Cramér-von-Mises, Anderson Darling, Anderson Darling - RT (right-tail), Anderson Darling - LT (left-tail), Anderson Darling - 2LT (left-tail second order), Kolmogorov and bayesian estimator with the prior Gamma. Some techniques to compare the estimators were used. Finally, applications were also performed, one for each univariate distribution, where the adjustment of some proposed distributions in relation to the database was tested.

Thesis (M. Phil.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 120-135).

Thesis (MSc)--University of Stellenbosch, 2008. / Bibliography. Also available via the Internet.

No description available.

Thesis (Ph. D.)--University of Washington, 1989. / Vita. Includes bibliographical references.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the Degree of Doctor of Philosophy. Johannesburg, August 2016. / There is a growing demand for small area estimates for policy and decision making, local planning and fund distribution. Surveys are generally designed to give representative estimates at national or regional level, but estimates of variables of interest are often also needed at the small area levels. These cannot be reliably obtained from the survey data as the sample sizes at these levels are too small. This problem is addressed by using small area estimation techniques. The main aim of this thesis is to develop confidence intervals (CIs) which are accurate to terms O(m–3/2 ) under the FH model using the Taylor series expansion. Rao (2003a), among others, notes that there is a situation in mixed model estimation that the estimates of the variance component of the random effect, A, can take negative values. In this case, Prasad and Rao (1990) consider ˆA = 0. Under this situation, the contribution of the mean squared error (MSE) estimate, assuming all parameters are known, becomes zero. As a solution, Rao (2003a) among others proposed a weighted estimator with fixed weights (i.e., wi = 12 ). In addition, if the MSE estimate is negative, we cannot construct CIs based on the empirical best linear unbiased predictor (EBLUP) estimates. Datta, Kubokawa, Molina and Rao (2011) derived the MSE estimator for the weighted estimator with fixed weights which is always positive. We use their MSE estimator to derive CIs based on this estimator to overcome the above difficulties. The other criticism of the MSE estimator is that it is not area-specific since it does not involve the direct estimator in its expression. Following Rao (2001), we propose area specific MSE estimators and use them to construct CIs. The performance of the proposed CIs are investigated via simulation studies and compared with the Cox (1975) and Prasad and Rao (1990) methods. Our simulation results show that the proposed CIs have higher coverage probabilities. These methods are applied to standard poverty and percentage of food expenditure measures estimated from the 2010/11 Household Consumption Expenditure survey and the 2007 census data sets. Keywords: Small area estimation, Weighted estimator with fixed weights, EBLUP, FH model, MSE, CI, Poverty, percentage of food expenditure / LG2017

No description available.

No description available.

The purpose of this study is to examine variances in the case of distributions obtained by truncating a given distribution at various points. In particular, the truncated distributions are restricted to nested increasing intervals, and the question is posed whether the variances of these distributions are monotonically increasing. The answer to this question is relevant to the use of conditional information for purposes of estimation and prediction. Several tables are presented in the thesis which provide evidence of the property of monotonic variance for nested increasing intervals of truncation in the case of univariate distributions., The Monte Carlo procedure is used to determine a table of standard deviations for the standard normal distribution with the same points of truncation reported by Clark(2). Clark's table is given intact, and it is used in comparison with the new table reported here as a check on the Monte Carlo procedure used in the present study. Distributions other than the standard normal distribution are examined as well, namely, a Pearson U-shaped distribution and a bimodal distribution consisting of a mixture or two Pearson distributions. Graphs of the U-shaped and bimodal distributions are given. A section is given in which dispersion for a bivariate case is examined in terms of the bivariate normal distribution. An interesting trend among the covariance matrices is observed in the data reported in that section. A separate computer program for each type of distribution was written and used to calculate the variances of the truncated distributions. FORTRAN programs and flow charts are presented in the Appendix. Explanation of the tables and procedures used to calculate the entries in the body of each table are given in each section as well as some discussion of the results presented. / Master of Science

University of Macau / Faculty of Science and Technology / Department of Mathematics