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Symmetry
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Symmetric and Asymmetric Bimodal Distributions with Applications
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Symmetric and Asymmetric Bimodal Distributions with Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 August 2023) | Viewed by 23538

Special Issue Editor

Dr. Héctor W. Gómez

E-Mail Website
Guest Editor
Departamento de Estadística y Ciencias de Datos, Universidad de Antofagasta, Antofagasta, Chile
Interests: distribution theory; classical and Bayesian inferencia; actuarial statistical; regression
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear colleagues,

The finite mixture of distributions is considered to be an standard methodology for data with two or more modes. This approach has some restrictions due of the possible identifiability problem.

This Special Issue is devoted to both original research articles and review articles, both theoretical and applied, related to bimodal or multimodal models, in symmetric and asymmetric distributions, applied to any areas of the knowledge.

Manuscripts on bimodal distributions generated with a basis on symmetrical or asymmetrical ones, which can compete with distribution mixtures, will be well received. Researchers are also invited to submit theoretical manuscripts showing bimodal distributions with their main properties, where parameter estimation will be performed based on a classical or Bayesian framework, with robust simulation studies on applied methodologies, such as regression models, time series, and survival analysis, among others.

Prof. Héctor W. Gómez
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • applications
  • asymmetric
  • bayesian
  • bimodal
  • maximum likelihood
  • simulation
  • symmetric

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Published Papers (7 papers)

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Research

13 pages, 549 KiB  
Article
A Bimodal Model Based on Truncation Positive Normal with Application to Height Data
by Héctor J. Gómez, Wilson E. Caimanque, Yolanda M. Gómez, Tiago M. Magalhães, Miguel Concha and Diego I. Gallardo
Symmetry 2022, 14(4), 665; https://doi.org/10.3390/sym14040665 - 24 Mar 2022
Cited by 1 | Viewed by 2364
Abstract
In this work, we propose a new bimodal distribution with support in the real line. We obtain some properties of the model, such as moments, quantiles, and mode, among others. The computational implementation of the model is presented in the tpn package of [...] Read more.
In this work, we propose a new bimodal distribution with support in the real line. We obtain some properties of the model, such as moments, quantiles, and mode, among others. The computational implementation of the model is presented in the tpn package of the software R. We perform a simulation study in order to assess the properties of the maximum likelihood estimators in finite samples. Finally, we present an application to a bimodal data set, where our proposal is compared with other models in the literature. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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10 pages, 363 KiB  
Article
An Asymmetric Bimodal Double Regression Model
by Yolanda M. Gómez, Diego I. Gallardo, Osvaldo Venegas and Tiago M. Magalhães
Symmetry 2021, 13(12), 2279; https://doi.org/10.3390/sym13122279 - 30 Nov 2021
Cited by 2 | Viewed by 1811
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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16 pages, 719 KiB  
Article
Generalizing Normality: Different Estimation Methods for Skewed Information
by Diego Carvalho do Nascimento, Pedro Luiz Ramos, David Elal-Olivero, Milton Cortes-Araya and Francisco Louzada
Symmetry 2021, 13(6), 1067; https://doi.org/10.3390/sym13061067 - 15 Jun 2021
Cited by 1 | Viewed by 1935
Abstract
Normality is the most commonly used mathematical supposition in data modeling. Nonetheless, even based on the law of large numbers (LLN), normality is a strong presumption, given that the presence of asymmetry and multi-modality in real-world problems is expected. Thus, a flexible modification [...] Read more.
Normality is the most commonly used mathematical supposition in data modeling. Nonetheless, even based on the law of large numbers (LLN), normality is a strong presumption, given that the presence of asymmetry and multi-modality in real-world problems is expected. Thus, a flexible modification in the normal distribution proposed by Elal-Olivero adds a skewness parameter called Alpha-skew-normal (ASN) distribution, which enables bimodality and fat-tail, if needed, although it is sometimes not trivial to estimate this third parameter (regardless of the location and scale). This work analyzed seven different statistical inferential methods towards the ASN distribution on synthetic data and historical data of water flux from 21 rivers (channels) in the Atacama region. Moreover, the contributions of this paper are related to the estimations of probability surrounding rivers’ flux levels in the surroundings of Copiapó city, which is the most economically important city of the third Chilean region and is known to be located in one of the driest areas on Earth (excluding the North and the South Poles). The results show the competitiveness of the MPS and RADE methods with respect to the MLE method, as well as their excellent performance. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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16 pages, 525 KiB  
Article
A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory
by Jimmy Reyes, Emilio Gómez-Déniz, Héctor W. Gómez and Enrique Calderín-Ojeda
Symmetry 2021, 13(4), 679; https://doi.org/10.3390/sym13040679 - 14 Apr 2021
Cited by 6 | Viewed by 2997
Abstract
There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of [...] Read more.
There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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27 pages, 12183 KiB  
Article
A New Bimodal Distribution for Modeling Asymmetric Bimodal Heavy-Tail Real Lifetime Data
by Nadeem S. Butt and Mohamed G. Khalil
Symmetry 2020, 12(12), 2058; https://doi.org/10.3390/sym12122058 - 11 Dec 2020
Cited by 7 | Viewed by 4036
Abstract
We introduced and studied a new generalization of the Burr type X distribution. Some of its properties were derived and numerically analyzed. The new density can be “right-skewed” and symmetric with “unimodal” and many “bimodal” shapes. The new failure rate can be “increasing,” [...] Read more.
We introduced and studied a new generalization of the Burr type X distribution. Some of its properties were derived and numerically analyzed. The new density can be “right-skewed” and symmetric with “unimodal” and many “bimodal” shapes. The new failure rate can be “increasing,” “bathtub,” “J-shape,” “decreasing,” “increasing-constant-increasing,” “reversed J-shape,” and “upside-down (reversed U-shape).” The usefulness and flexibility of the new distribution were illustrated by means of four asymmetric bimodal right- and left-heavy tail real lifetime data. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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13 pages, 804 KiB  
Article
An Asymptotic Test for Bimodality Using The Kullback–Leibler Divergence
by Javier E. Contreras-Reyes
Symmetry 2020, 12(6), 1013; https://doi.org/10.3390/sym12061013 - 16 Jun 2020
Cited by 5 | Viewed by 3145
Abstract
Detecting bimodality of a frequency distribution is of considerable interest in several fields. Classical inferential methods for detecting bimodality focused in third and fourth moments through the kurtosis measure. Nonparametric approach-based asymptotic tests (DIPtest) for comparing the empirical distribution function with a unimodal [...] Read more.
Detecting bimodality of a frequency distribution is of considerable interest in several fields. Classical inferential methods for detecting bimodality focused in third and fourth moments through the kurtosis measure. Nonparametric approach-based asymptotic tests (DIPtest) for comparing the empirical distribution function with a unimodal one are also available. The latter point drives this paper, by considering a parametric approach using the bimodal skew-symmetric normal distribution. This general class captures bimodality, asymmetry and excess of kurtosis in data sets. The Kullback–Leibler divergence is considered to obtain the statistic’s test. Some comparisons with DIPtest, simulations, and the study of sea surface temperature data illustrate the usefulness of proposed methodology. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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18 pages, 1195 KiB  
Article
Likelihood-Based Inference for the Asymmetric Beta-Skew Alpha-Power Distribution
by Guillermo Martínez-Flórez, Roger Tovar-Falón and Marvin Jimémez-Narváez
Symmetry 2020, 12(4), 613; https://doi.org/10.3390/sym12040613 - 13 Apr 2020
Cited by 8 | Viewed by 3118
Abstract
This paper introduces a new family of asymmetric distributions that allows to fit unimodal as well as bimodal and trimodal data sets. The model extends the normal model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic [...] Read more.
This paper introduces a new family of asymmetric distributions that allows to fit unimodal as well as bimodal and trimodal data sets. The model extends the normal model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new distribution are studied in detail. The problem of estimating parameters is addressed by considering the maximum likelihood method and Fisher information matrix is derived. A small Monte Carlo simulation study is conducted to examine the performance of the obtained estimators. Finally, two data set are considered to illustrate the developed methodology. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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