A Bimodal Extension of the Generalized Gamma Distribution

Çankaya, Mehmet Niyazi; Bulut, Y. Murat; Doğru, Fatma Zehra; Arslan, Olçay

doi:10.15446/rce.v38n2.51666

Cited by 16 publications

(18 citation statements)

References 19 publications

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“…Rényi entropy can be easily deduced from Tsallis by relation (14). Moreover, in Appendix, we also derive a hybrid entropy for ε-skew exponential power distribution [39], which is a special class of bimodal distributions, recently introduced by Ç ankaya et al [40]. This class of distribution finds its place in the mathematical and physical problems, especially in statistical estimation.…”

Section: Continuous Hybrid Entropymentioning

confidence: 99%

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On statistical properties of Jizba–Arimitsu hybrid entropy

Çankaya

Korbel

2017

Physica A: Statistical Mechanics and its Applications

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Jizba-Arimitsu entropy (also called hybrid entropy) combines axiomatics of Rényi and Tsallis entropy. It has many common properties with them, on the other hand, some aspects as e.g., MaxEnt distributions, are completely different from the former two entropies. In this paper, we demonstrate the statistical properties of hybrid entropy, including the definition of hybrid entropy for continuous distributions, its relation to discrete entropy and calculation of hybrid entropy for some well-known distributions. Additionally, definition of hybrid divergence and its connection to Fisher metric is also discussed. Interestingly, the main properties of continuous hybrid entropy and hybrid divergence are completely different from measures based on Rényi and Tsallis entropy. This motivates us to introduce average hybrid entropy, which can be understood as an average between Tsallis and Rényi entropy

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Section: Continuous Hybrid Entropymentioning

confidence: 99%

“…The distribution was originally introduced in [39,40] as p(x; µ, σ, α, β, η, ε) = αβ 2ση 1/α Γ( where α, β, η, σ > 0, µ ∈ R and ε ∈ [−1, 1]. Parameters µ and σ are location and scale parameters, respectively.…”

Section: Acknowledgementsmentioning

confidence: 99%

On statistical properties of Jizba–Arimitsu hybrid entropy

Çankaya

Korbel

2017

Physica A: Statistical Mechanics and its Applications

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“…Besides of reparametrizing the skew parameter in [14], heavy-tailedness asymmetry is managed by two different tail exponents on different sides of the location parameter µ. From another perspective, an interest has risen for bimodal skewed distributions [15].…”

Section: Distributionmentioning

confidence: 99%

A multimodal asymmetric exponential power distribution: Application to risk measurement for financial high-frequency data

Thibault¹,

Bondon²

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Interest in risk measurement for high-frequency data has increased since the volume of high-frequency trading stepped up over the two last decades. This paper proposes a multimodal extension of the Exponential Power Distribution (EPD), called the Multimodal Asymmetric Exponential Power Distribution (MAEPD). We derive moments and we propose a convenient stochastic representation of the MAEPD. We establish consistency, asymptotic normality and efficiency of the maximum likelihood estimators (MLE). An application to risk measurement for high-frequency data is presented. An autoregressive moving average multiplicative component generalized autoregressive conditional heteroskedastic (ARMA-mcsGARCH) model is fitted to Financial Times Stock Exchange (FTSE) 100 intraday returns. Performances for Value-at-Risk (VaR) and Expected Shortfall (ES) estimation are evaluated. We show that the MAEPD outperforms commonly used distributions in risk measurement.

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“…The properties of BEP distribution are few when BEP is compared with distribution proposed by [ 29 ] because BEP has the same level of peaks around location on the real line, and it is also symmetric on both sides of the location. The shape of peakedness around location on the real line is modelled by only one parameter; however, two parameters are added in order to model different modes from distribution on the real line [ 29 ]. Two parameters controlling fitting the shape of peakedness and two parameters controlling fitting the height of bimodality will be used together.…”

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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A Bimodal Extension of the Generalized Gamma Distribution

Cited by 16 publications

References 19 publications

On statistical properties of Jizba–Arimitsu hybrid entropy

On statistical properties of Jizba–Arimitsu hybrid entropy

A multimodal asymmetric exponential power distribution: Application to risk measurement for financial high-frequency data

Asymmetric Bimodal Exponential Power Distribution on the Real Line

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