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The Modi Exponentiated Exponential Distribution

Journal of Data Analysis and Information Processing 2023年第4期11卷 341-359页

作者： Antoine Dieudonné Ndayisaba leo odiwuor odongo Anthony Ngunyi Department of Mathematics Pan African University Institute for Basic Sciences Technology and Innovation (PAUSTI) Nairobi Kenya Department of Mathematics and Actuarial Science Kenyatta University (KU) Nairobi Kenya Department of Mathematics Statistics and Actuarial Sciences Dedan Kimathi University of Technology (De KUT) Nairobi Kenya

In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.

关键词： Modi Family Exponentiated Exponential Distribution Maximum Likelihood Estimation Order Statistics Moments Quantile Function

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Marshall-Olkin Exponentiated Fréchet Distribution

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Journal of Data Analysis and Information Processing 2023年第3期11卷 262-292页

作者： Aurise Niyoyunguruza leo odiwuor odongo Euna Nyarige Alexis Habineza Abdisalam Hassan Muse Department of Mathematics Pan African University Institute for Basic Sciences Technology and Innovation (PAUSTI) Nairobi Kenya Department of Mathematics and Actuarial Science Kenyatta University (KU) Nairobi Kenya Department of Mathematics and Statistics Machakos University Machakos Kenya

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.

关键词： Exponentiated Fréchet Distribution Maximum Likelihood Estimation Marshall-Olkin Family

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