The Weibull distribution in the study of lifetime

• Grant number: 09/07784-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2009
• End date: June 30, 2010
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Vicente Garibay Cancho
• Grantee: Bao Yiqi
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The objective of this project is to study characteristics of the Weibull distribution, such as the probability density function, the function of survival, function risk, the fashion and the median. This is a very important distribution used in the analysis of survival. The procedure for estimation of parameter of the model is based on the method of maximum likelihood. We also work in three methods of constructing confidence intervals for the parameters and the p-th quantile of the Weibull model, it is the range of asymptotic confidence intervals and p-bootstrap and bootstrap-t, which are based on the process known as bootstrap resampling (Efron & Tibshirani, 1993). Assess the probability of coverage of these three ways of constructing the confidence intervals considering various sample sizes and different percentage of censored observations.