Correção de viés do Modelo de Gumbel com censura Tipo I e Tipo II

Abstract

In this thesis, we use the model of Gumbel; Initially we had the Fisher information matrix and we write in a matrix form, then calculated the second- and third-order cumulants later derive the second order cumulants with respect to the parameters. Then we subtract the derivatives of the second order cumulants the third order cumulants and replace these values in the expression of Cox and Snell to obtain the correction of bias.We use the formula found in Cox and Snell (1968), because from what outcome we can define a corrected estimator ˜θa = ˆθa − ˆB(ˆθa), where ˆB (ˆθa) it is the estimated bias ˆθa, where ˜θa has order bias O(n−2). As soon as the sample size n increases, we expect the bias ˜θa approaches zero faster than the bias ˆθa. We will correct the bias for the model with censorship Gumbel type I and type II.