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Bayesian Analysis of the Epsilon Skew Exponential Power Distribution |
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PP: 97-108 |
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doi:10.18576/jsapl/070301
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Author(s) |
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Michael Weldensea,
Hassan Elsalloukh,
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Abstract |
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| The Epsilon Skew Exponential Power Distribution (ESEP) that was introduced by Elsalloukh [1] is an asymmetric distribution used for modeling asymmetric data. The ESEP includes Normal, Laplace, Epsilon Skew Normal (ESN), and Epsilon Skew Laplace (ESL) as particular cases, [1]. In the present study, since the ESEP distribution encompasses members with skewed and symmetric distributions, we perform and investigate the Bayesian analysis of this distribution using the methods of latent variables and uniform scale mixture for implementing the most common MCMC algorithm known as Gibbs sampling. Furthermore, we develop the posterior distributions and the full conditional distributions of each parameter of the ESEP using Jeffrey’s non-informative and informative priors for each parameter. Finally, we provide examples to show the fitting accuracy and strength of the ESEP distribution compared to other distributions used in literature. |
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