Marshall-Olkin Exponentiated Fréchet Distribution
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Date
2023
Authors
Niyoyunguruza, Aurise
Odongo, Leo Odiwuor
Nyarige, Euna
Habineza, Alexis
Muse, Abdisalam Hassan
Journal Title
Journal ISSN
Volume Title
Publisher
Scientific Research Publishing Inc
Abstract
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.
Description
article
Keywords
Exponentiated Fréchet Distribution, Maximum Likelihood Estimation, Marshall-Olkin Family
Citation
Niyoyunguruza, A., Odongo, L.O., Nyarige, E., Habineza, A. and Muse, A.H. (2023) Marshall-Olkin Exponentiated Fréchet Distribution. Journal of Data Analysis and Information Processing, 11, 262-292. https://doi.org/10.4236/jdaip.2023.113014