For interval-censored and truncated failure time data, the truncation ratio is unknown. In this paper, we propose an algorithm, similar to Turnbull's, to estimate the parameters. The truncation ratio for the interval-censored and truncated failure time data can also be estimated by the convergence result of the algorithm. A simulation study is proposed to compare with Turnbull (1976). Our algorithm seems to have better result.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-27T13:45:09Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Paulo Roberto de Oliveira - 2014.pdf: 3459807 bytes, checksum: b199bab67e773541a99d42adfc9dce03 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-28T11:28:00Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Paulo Roberto de Oliveira - 2014.pdf: 3459807 bytes, checksum: b199bab67e773541a99d42adfc9dce03 (MD5) / Made available in DSpace on 2015-01-28T11:28:00Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Paulo Roberto de Oliveira - 2014.pdf: 3459807 bytes, checksum: b199bab67e773541a99d42adfc9dce03 (MD5) Previous issue date: 2014-07-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Many monthly, others weekly play in lottery games ignoring the randomness of the results, believing in luck or strategies that are sold to them in books about games. This monograph aims to show some concepts of probability and statistics unexplored in high school and also day to day situations that contain mathematical concepts of probability more accessible to this level of education showing some mathematical theories applied in practice games. Concepts will be discussed here: some probability distributions, their hope and variance, as well as lottery games and their probability calculations. Probability distributions will be calculated and listed in situations created from models of urns with two colors of balls, always having green as the color whose extraction will be considered successful and the red, whose extraction will be considered a failure. Now extractions with replacement balls will be made and sometimes extractions will be done without replacing them. Also, there is the case where new balls are added to both colors or one color. / Muitos jogam mensalmente, outros semanalmente, em jogos de loterias desconhecendo a aleatoriedade dos seus resultados, acreditando na sorte ou em estratégias que lhes são vendidas em livros sobre jogos. A presente monogra a tem como objetivo mostrar alguns conceitos da Probabilidade e Estatística não explorados no Ensino Médio e também situações do dia a dia que contenham conceitos matemáticos sobre Probabilidade mais acessíveis a este nível de ensino, mostrando um pouco de teorias matemáticas aplicadas na prática de jogos. Serão conceitos aqui discutidos: algumas distribuições de probabilidade, sua esperan ça e variância, além de jogos de loterias e seus cálculos de probabilidade. As distribuições de probabilidade serão enunciadas e calculadas em situações criadas a partir de modelos de urnas com duas cores de bolas, tendo sempre o verde como a cor cuja extração será considerada sucesso e, o vermelho, cuja extração será considerada insucesso. Ora serão feitas extrações com reposições das bolas e ora serão feitas extrações sem a reposição das mesmas. Também, há o caso em que serão adicionadas novas bolas de ambas as cores ou uma cor apenas.

In this article, we make inferences for the Weibull parameters and propose two test statistics for the comparison of two Weibull distributions based on interval-censored data. However, the distributions of the two statistics are unknown and not easy to obtain, therefore a simulation study is necessary. An urn model in the simulation of interval-censored data was proposed by Lee (1999) to select random intervals. Then we propose a simulation procedure with urn model to obtain approximately the quantiles of the two statistics. We demonstrate an example in AIDS study to illustrate how the tests can be applied to the infection time distributions of AIDS.

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