We introduce a new three-parameter lifetime model called the odd Birnbaum-Saunders distribution. We construct an extended regression model based on the logarithm of the new distribution, which can be applied to censored data and be more effective in analyzing real data. Maximum likelihood estimation of the model parameters of the new regression model is discussed for complete and censored samples. A modified deviance residual is proposed to assess departures from the log-odd Birnbaum-Saunders error assumption and to detect outlying observations. Real data sets are analyzed for illustrative purposes.
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