An Asymmetric Bimodal Distribution with Application to Quantile Regression

Gómez, Yolanda M.; Gómez–Déniz, Emilio; Venegas, Osvaldo; Gallardo, Diego I.; Gómez, Héctor W.

doi:10.3390/sym11070899

Cited by 6 publications

(5 citation statements)

References 19 publications

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“…Other symmetric/asymmetric unimodal/bimodal distributions are also considered to illustrate that the LGB distribution or some of its special cases may have a better fit than other distributions in the literature. Specifically, the odd log-logistic skew-normal (OLLSN) [28] and gamma sinh-Cauchy (GSC) [29] distributions are considered. Like the LGB distribution, these distributions have four parameters: two shape parameters (which together control skewness and bimodality), a location parameter, and a scale parameter.…”

Section: Discussionmentioning

confidence: 99%

A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation

2021

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The generalized bimodal distribution is especially efficient in modeling univariate data exhibiting symmetry and bimodality. However, its performance is poor when the data show important levels of skewness. This article introduces a new unimodal/bimodal distribution capable of modeling different skewness levels. The proposal arises from the recently introduced Lambert transformation when considering a generalized bimodal baseline distribution. The bimodal-normal and generalized bimodal distributions can be derived as special cases of the new distribution. The main structural properties are derived and the parameter estimation is carried out under the maximum likelihood method. The behavior of the estimators is assessed through simulation experiments. Finally, two applications are presented in order to illustrate the utility of the proposed distribution in data modeling in different real settings.

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Section: Discussionmentioning

confidence: 99%

A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation

2021

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“…In other words, the bmi and lbm explain both the q-th quantile of Bfat and the scale of the distribution. The same structure of covariates was considered in [13], but without modeling the scale parameter; i.e., considering β 22 (q) = β 23 (q) = 0. We refer to those models as GSC and GSC 0 for the cases where σ is modeled and not modeled, respectively.…”

Section: Applicationmentioning

confidence: 99%

“…Alternatively, the most workable practical method is to use a distribution which already has bimodal properties. For the latter situation, we introduce the gamma-sinh Cauchy (GSC) distribution, proposed by [13]. We note that the initials GSC can be found in the literature as an acronym for Generalized Skew-Cauchy, and readers should be aware of this when reviewing the literature.…”

Section: Introductionmentioning

confidence: 99%

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An Asymmetric Bimodal Double Regression Model

et al. 2021

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In this paper, we introduce an extension of the sinh Cauchy distribution including a double regression model for both the quantile and scale parameters. This model can assume different shapes: unimodal or bimodal, symmetric or asymmetric. We discuss some properties of the model and perform a simulation study in order to assess the performance of the maximum likelihood estimators in finite samples. A real data application is also presented.

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“…In empirical analyses, analyzed data are frequently bimodal and cannot be modeled by unimodal distributions [ 49 ]. Bimodality means that a given distribution has two modes and a large proportion of observations with large distances from the middle of the distribution [ 50 ].…”

Section: Bimodal Distributionmentioning

confidence: 99%

Weighted Quantile Regression Forests for Bimodal Distribution Modeling: A Loss Given Default Case

Gostkowski

Gajowniczek

2020

Entropy

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Due to various regulations (e.g., the Basel III Accord), banks need to keep a specified amount of capital to reduce the impact of their insolvency. This equity can be calculated using, e.g., the Internal Rating Approach, enabling institutions to develop their own statistical models. In this regard, one of the most important parameters is the loss given default, whose correct estimation may lead to a healthier and riskless allocation of the capital. Unfortunately, since the loss given default distribution is a bimodal application of the modeling methods (e.g., ordinary least squares or regression trees), aiming at predicting the mean value is not enough. Bimodality means that a distribution has two modes and has a large proportion of observations with large distances from the middle of the distribution; therefore, to overcome this fact, more advanced methods are required. To this end, to model the entire loss given default distribution, in this article we present the weighted quantile Regression Forest algorithm, which is an ensemble technique. We evaluate our methodology over a dataset collected by one of the biggest Polish banks. Through our research, we show that weighted quantile Regression Forests outperform “single” state-of-the-art models in terms of their accuracy and the stability.

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An Asymmetric Bimodal Distribution with Application to Quantile Regression

Cited by 6 publications

References 19 publications

A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation

A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation

An Asymmetric Bimodal Double Regression Model

Weighted Quantile Regression Forests for Bimodal Distribution Modeling: A Loss Given Default Case

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