Asymmetric Bimodal Exponential Power Distribution on the Real Line

Çankaya, Mehmet Niyazi

doi:10.3390/e20010023

Cited by 13 publications

(4 citation statements)

References 48 publications

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“…By using the integral kernels in Ref. [10], we obtain following result for the integral of middle part in Eq. (2.28) given by…”

Section: Huber's ρ H Complexity Based On Kl Divergence For the Normal...mentioning

confidence: 99%

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Information Complexity Criterion for Model Selection in Robust Regression Using A New Robust Penalty Term

Pamukçu¹,

Çankaya²

2020

Preprint

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Model selection is basically a process of finding the best model from the subset of models in which the explanatory variables are effective on the response variable. The log likelihood function for the lack of fit term and a specified penalty term are used as two parts in a model selection criteria. In this paper, we derive a new tool for the model selection in robust regression. We introduce a new definition of relative entropy based on objective functions. Due to the analytical simplicity, we use Huber's objective function ρH and propose our specified penalty term C ρ H 0 to derive new Information Complexity Criterion (RICOM P C ρ H 0 ) as a robust model selection tool. Additionally, by using the properties of C ρ H 0 , we propose a new value of tuning parameter called kC 0 for the Huber's ρH. If a contamination to normal distribution exists, RICOM P C ρ H 0 chooses the true model better than the rival ones. Monte Carlo Simulation studies are carried out to show the utility both of kC 0 and RICOM P C ρ H 0 .A real data example is also given.

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“…By using the integral kernels in Ref. [10], we obtain following result for the integral of middle part in Eq. (2.28) given by…”

Section: Huber's ρ H Complexity Based On Kl Divergence For the Normal...mentioning

confidence: 99%

“…We use the prepared kernels from Ref. [10] to calculate the integrals of F and R. The underlying distribution of expectation is chosen as normal distribution.…”

Section: Amentioning

confidence: 99%

Information Complexity Criterion for Model Selection in Robust Regression Using A New Robust Penalty Term

Pamukçu¹,

Çankaya²

2020

Preprint

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“…In this section, we apply the proposed DLN distribution to a real data set from a DNA microarray reported in [19]. According to Wikipedia, "A DNA microarray (also commonly known as DNA chip or biochip) is a collection of microscopic DNA spots attached to a solid surface.…”

Section: Applicationmentioning

confidence: 99%

A Bimodal Extension of the Log-Normal Distribution on the Real Line with an Application to DNA Microarray Data

Alfahad,

Ghitany,

Alothman

et al. 2023

Mathematics

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A bimodal double log-normal distribution on the real line is proposed using the random sign mixture transform. Its associated statistical inferences are derived. Its parameters are estimated by the maximum likelihood method. The performance of the estimators and the corresponding confidence intervals is checked by simulation studies. Application of the proposed distribution to a real data set from a DNA microarray is presented.

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“…There are different degrees of mixing via Maxwell distribution and the expression which can help us to have different forms of modality of function for generating modality via compounding distributions [9,12]. The bimodal form on the positive part of the real line produces a trimodal form when it is reflected to the negative part of the real line via mirror imaging [1,13,14,15]. The different degree of bimodality, i.e.…”

Section: Introductionmentioning

confidence: 99%

A General Class of Trimodal Distributions: Properties and Inference

Vila¹,

Victor²,

Çankaya³

et al. 2022

Preprint

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The modality is important topic for modelling. Using parametric models is an efficient way when real data set shows trimodality. In this paper we propose a new class of trimodal probability distributions, that is, probability distributions that have up to three modes. Trimodality itself is achieved by applying a proper transformation to density function of certain continuous probability distributions. At first, we obtain preliminary results for an arbitratry density function g(x) and, next, we focus on the Gaussian case, studying trimodal Gaussian model more deeply. The Gaussian distribution is applied to produce the trimodal form of Gaussian known as normal distribution. The tractability of analytical expression of normal distribution, and properties of the trimodal normal distribution are important reasons why we choose normal distribution. Furthermore, the existing distributions should be improved to be capable of modelling efficiently when there exists a trimodal form in a data set. After new density function is proposed, estimating its parameters is important. Since Mathematica 12.0 software has optimization tools and important modelling techniques, computational steps are performed by using this software. The bootstrapped form of real data sets are applied to show the modelling ability of the proposed distribution when real data sets show trimodality.

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Asymmetric Bimodal Exponential Power Distribution on the Real Line

Cited by 13 publications

References 48 publications

Information Complexity Criterion for Model Selection in Robust Regression Using A New Robust Penalty Term

Information Complexity Criterion for Model Selection in Robust Regression Using A New Robust Penalty Term

A Bimodal Extension of the Log-Normal Distribution on the Real Line with an Application to DNA Microarray Data

A General Class of Trimodal Distributions: Properties and Inference

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