Bimodal skew-symmetric normal distribution

Hassan, Mohamed Yusuf; El-Bassiouni, M.Y.

doi:10.1080/03610926.2014.882950

Cited by 22 publications

(19 citation statements)

References 26 publications

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“…Further, in literature, there exist some studies which include multimodal distributions. For instance, some of them are [43][44][45][46][47][48][49][50] etc. These proposed distributions can be used to model data sets which have modality.…”

Section: Discussionmentioning

confidence: 99%

Modeling Human Development Index Using Finite Mixtures of Distributions

Doğru

2017

ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY a - Applied Sciences and Engineering

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The Human Development Index (HDI) measures the development of a country which was designed by the United Nations Development Programme (UNDP). Since the values of HDI for different countries show differences according to the development of a country, the distribution of HDI may have one more mode, thick tail or skewness. Therefore, we can use mixtures of distributions to model the HDI data set to handle modality, heavy-tailedness and/or skewness. In this study, we propose to model the data set from the HDI report 2015 for 188 countries with finite mixtures of distributions. We give the basic scheme of the maximum likelihood (ML) estimation using Expectation-Maximization (EM) algorithm for the finite mixture model. To obtain the best model for HDI data set, we first find the appropriate cluster number using model-based clustering. Then, we use the finite mixture models obtained from some symmetric and/or heavy-tailed and skew and/or heavytailed distributions to find the best model for HDI data set.

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Section: Discussionmentioning

confidence: 99%

Modeling Human Development Index Using Finite Mixtures of Distributions

Doğru

2017

ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY a - Applied Sciences and Engineering

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“…A class of generalized bimodal distributions that extends the GB distribution can be found in [2]. This class is defined by the cdf F(x) = Φ(x) − α(x) φ(x), where α(x) is a linear function of x.…”

Section: Missing Citationmentioning

confidence: 99%

“…This class is defined by the cdf F(x) = Φ(x) − α(x) φ(x), where α(x) is a linear function of x. Thus, the GB distribution (with cdf given in Equation ( 2)) can be derived as a special case of the class proposed by [2] when α(x) = x/(1 + γ).…”

Section: Missing Citationmentioning

confidence: 99%

Correction: Iriarte et al. A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation. Symmetry 2021, 13, 269

2021

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“…The different bimodal and skew distributions have been proposed over the last decade to construct flexible distributions. The proposed distributions are in [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ] and references therein via using different generating techniques [ 27 ] to get a probability density function (PDF). In these distributions,

-skew form of gamma distribution on the real line was proposed by [ 5 , 6 ].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Bimodal Exponential Power Distribution on the Real Line

Çankaya

2018

Entropy

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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.

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Bimodal skew-symmetric normal distribution

Cited by 22 publications

References 26 publications

Modeling Human Development Index Using Finite Mixtures of Distributions

Modeling Human Development Index Using Finite Mixtures of Distributions

Correction: Iriarte et al. A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation. Symmetry 2021, 13, 269

Asymmetric Bimodal Exponential Power Distribution on the Real Line

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