Title: The Long Term Fréchet distribution: Estimation, Properties and its Application,
Abstract: In this paper a new long-term survival distribution is proposed. The so
called long term Fréchet distribution allows us to fit data where a part of
the population is not susceptible to the event of interest. This model may be
used, for example, in clinical studies where a portion of the population can be
cured during a treatment. It is shown an account of mathematical properties of
the new distribution such as its moments and survival properties. As well is
presented the maximum likelihood estimators (MLEs) for the parameters. A
numerical simulation is carried out in order to verify the performance of the
MLEs. Finally, an important application related to the leukemia free-survival
times for transplant patients are discussed to illustrates our proposed
distribution