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Entropy 2018, 20(1), 23; https://doi.org/10.3390/e20010023

Asymmetric Bimodal Exponential Power Distribution on the Real Line

1
Department of International Trading, School of Applied Sciences, Uşak University, Uşak 64200, Turkey
2
Department of Statistics, Faculty of Arts and Sciences, Uşak University, Uşak 64200, Turkey
Received: 1 November 2017 / Revised: 29 December 2017 / Accepted: 1 January 2018 / Published: 3 January 2018
(This article belongs to the Section Information Theory, Probability and Statistics)
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Abstract

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters that fit the shape of peakedness in bimodality on the real line. The special values of peakedness parameters of the distribution are a combination of half Laplace and half normal distributions on the real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and other distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data. A brief simulation study is presented. View Full-Text
Keywords: asymmetric bimodality; bimodal exponential power distribution; modelling; generalized Gaussian distribution asymmetric bimodality; bimodal exponential power distribution; modelling; generalized Gaussian distribution
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Çankaya, M.N. Asymmetric Bimodal Exponential Power Distribution on the Real Line. Entropy 2018, 20, 23.

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