%0 Journal Article
%T Marshall-Olkin Exponentiated Fréchet Distribution
%A Aurise Niyoyunguruza
%A Leo Odiwuor Odongo
%A Euna Nyarige
%A Alexis Habineza
%A Abdisalam Hassan Muse
%J Journal of Data Analysis and Information Processing
%P 262-292
%@ 2327-7203
%D 2023
%I Scientific Research Publishing
%R 10.4236/jdaip.2023.113014
%X In this paper, a new distribution called Marshall-Olkin Exponentiated Fr¨Śchet
distribution (MOEFr) is proposed. The goal is to increase the flexibility of
the existing Exponentiated Fr¨Śchet 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 <span>function, reversed hazard
rate function, cumulative hazard function, odds functio</span>n, 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 Exponen<span>tiated
Fr¨Śchet</span></span><span style=\"font-family:&quot;\"> </span><span style=\"font-family:&quot;\">(EFr), Marshall-Olkin Fr¨Śchet</span><span style=\"font-family:&quot;\"> </span><span style=\"font-family:&quot;\">(MOFr), Beta Exponential Fr¨Śchet</span><span style=\"font-family:&quot;\"> </span><span style=\"font-family:&quot;\">(BEFr), Beta Fr¨Śchet</span><span style=\"font-family:&quot;\"> </span><span style=\"font-family:&quot;\">(BFr) and Fr¨Śchet</span><span style=\"font-family:&quot;\"> </span><span style=\"font-family:&quot;\">(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.
%K Exponentiated Fr&#233
%K chet Distribution
%K Maximum Likelihood Estimation
%K Marshall-Olkin Family
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=126403