In this paper, a new distribution called Marshall-Olkin Exponentiated Fréchet
distribution (MOEFr) is proposed. The goal is to increase the flexibility of
the existing Exponentiated Fréchet distribution by including an extra shape
parameter, resulting into a more flexible distribution that can provide a
better fit to various data sets than the baseline distribution. A generator
method introduced by Marshall and Olkin is used to develop the new
distribution. Some properties of the new distribution such as hazard rate
function, survival function, reversed hazard
rate function, cumulative hazard function, odds function, quantile
function, moments and order statistics are derived. The maximum likelihood
estimation is used to estimate the model parameters. Monte Carlo simulation is
used to evaluate the behavior of the estimators through the average bias and
root mean squared error. The new distribution is fitted and compared with some
existing distributions such as the Exponentiated
Fréchet(EFr), Marshall-Olkin Fréchet(MOFr), Beta Exponential Fréchet(BEFr), Beta Fréchet(BFr) and Fréchet(Fr) distributions, on three data sets, namely
Bladder cancer, Carbone and Wheaton River data sets. Based on the
goodness-of-fit statistics and information criteria values, it is demonstrated
that the new distribution provides a better fit for the three data sets than
the other distributions considered in the study.
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