The Exponentiated Weibull Family

The purpose of this work is to introduce extensive study for the exponentiated Weibull family and to promote its use (as statistical family of models) in applications in reliability and survival analysis. The text of this book is useful for undergraduate and graduate students of mathematical statistics. The book concentrates on the exponentiated Weibull distribution as a model whose failure rate function possesses monotone and non-monotone curves for certain values of the parameters. New statistical characterizations for the density function of the distribution are discussed. Also, we show that this distribution may have a failure rate (mean residual life) function which is bathtub (upside-down bathtub) shaped or it may have a failure rate (mean residual life) which is upside-down bathtub (bathtub) shaped. The capability and flexibility of the distribution in classical and Bayesian inferences are studied. In addition, prediction for the behavior of future observations from the distribution is also considered. Numerical examples are included to illustrate some theoretical statements.