# Bimodal skew-symmetric normal distribution

@article{Hassan2016BimodalSN, title={Bimodal skew-symmetric normal distribution}, author={M.Y. Hassan and Mohamed Y. El-Bassiouni}, journal={Communications in Statistics - Theory and Methods}, year={2016}, volume={45}, pages={1527 - 1541} }

ABSTRACT We introduce a new parsimonious bimodal distribution, referred to as the bimodal skew-symmetric Normal (BSSN) distribution, which is potentially effective in capturing bimodality, excess kurtosis, and skewness. Explicit expressions for the moment-generating function, mean, variance, skewness, and excess kurtosis were derived. The shape properties of the proposed distribution were investigated in regard to skewness, kurtosis, and bimodality. Maximum likelihood estimation was considered… Expand

#### 13 Citations

An Asymptotic Test for Bimodality Using The Kullback-Leibler Divergence

- Mathematics, Computer Science
- Symmetry
- 2020

Comparisons with DIPtest, simulations, and the study of sea surface temperature data illustrate the usefulness of proposed methodology, by considering a parametric approach using the bimodal skew-symmetric normal distribution. Expand

On some properties of the bimodal normal distribution and its bivariate version

- Mathematics
- 2021

In this work, we derive some novel properties of the bimodal normal distribution. Some of its mathematical properties are examined. We provide a formal proof for the bimodality and assess… Expand

Skewed and Flexible Skewed Distributions: A Modern Look at the Distribution of BMI

- Mathematics
- 2017

ABSTRACT The purpose of this study is to find distributions that best model body mass index (BMI) data. BMI has become a standard health indicator and numerous studies have been done to examine the… Expand

Asymmetric Bimodal Exponential Power Distribution on the Real Line

- Mathematics, Computer Science
- Entropy
- 2018

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… Expand

Asymmetric Bimodal Exponential Power Distribution 2 on Real Line 3

- 2017

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the 8 generalized gamma distribution to the real line via adding two parameters which fit the shape of 9 peakedness in… Expand

On the robustness of an epsilon skew extension for Burr III distribution on the real line

- Mathematics, Computer Science
- Comput. Stat.
- 2019

The epsilon skew extension of Burr III (ESBIII) distribution with only three parameters can provide adequate fits for data sets that may have heavy-tailedness, skewness, unimodality or bimodality. Expand

General methods for analyzing bounded proportion data

- Mathematics
- 2017

This thesis introduces two general classes of models for analyzing proportion response variable when the response variable Y can take values between zero and one, inclusive of zero and/or one. The… Expand

Modeling Human Development Index Using Finite Mixtures of Distributions

- Materials Science
- 2017

The Human Development Index (HDI) measures development of a country which was designed by the United Nations Development Programme (UNDP). Since the values of HDI for different countries show… Expand

A Worst-Case Risk Measure by G-VaR

- 2018

A kind of worst-case value-at-risk, GVaR, is defined to measure risk incorporating model uncertainty. Compared with most extant notions of worst-case VaR, GVaR can be computed by an explicit formula,… Expand

A Worst-Case Risk Measure by G-VaR

- 2021

G-VaR, which is a type of worst-case value-at-risk (VaR), is defined as measuring risk incorporating model uncertainty. Compared with most extant notions of worst-case VaR, G-VaR can be computed… Expand

#### References

SHOWING 1-10 OF 45 REFERENCES

Generalized skew normal model

- Mathematics
- 2004

The skew normal distribution proposed by Azzalini (1985) can be a suitable model for the analysis of data exhibiting a unimodal density function having some skewness present, a structure often… Expand

Robust mixture modeling based on scale mixtures of skew-normal distributions

- Mathematics, Computer Science
- Comput. Stat. Data Anal.
- 2010

Some simulation studies are presented to show the advantage of this flexible class of probability distributions in clustering heterogeneous data and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Expand

Bayesian Modeling Using a Class of Bimodal Skew-Elliptical Distributions

- Mathematics
- 2009

Abstract We consider Bayesian inference using an extension of the family of skew-elliptical distributions studied by Azzalini [1985. A class of distributions which includes the normal ones. Scand. J.… Expand

Bimodal extension based on the skew-normal distribution with application to pollen data

- Mathematics
- 2011

This paper considers an extension to the skew-normal model through the inclusion of an additional parameter which can lead to both uni- and bi-modal distributions. The paper presents various basic… Expand

Skewed multivariate models related to hidden truncation and/or selective reporting

- Mathematics
- 2002

The univariate skew-normal distribution was introduced by Azzalini in 1985 as a natural extension of the classical normal density to accommodate asymmetry. He extensively studied the properties of… Expand

An Extension of the Epsilon-Skew-Normal Distribution

- Mathematics
- 2010

This article is related with the probabilistic and statistical properties of an parametric extension of the so-called epsilon-skew-normal (ESN) distribution introduced by Mudholkar and Hutson (2000),… Expand

Flexible Class of Skew‐Symmetric Distributions

- Mathematics
- 2004

Abstract. We propose a flexible class of skew‐symmetric distributions for which the probability density function has the form of a product of a symmetric density and a skewing function. By… Expand

Statistical applications of the multivariate skew normal distribution

- Mathematics
- 1999

Azzalini and Dalla Valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the… Expand

The epsilon-skew-normal distribution for analyzing near-normal data

- Mathematics
- 2000

Abstract A family of asymmetric distributions, which first appeared in Fechner (1897, Kollectivmasslehre. Leipzig, Engleman) is reparameterized using a skewness parameter e and named the… Expand

The multivariate skew-normal distribution

- Mathematics
- 1996

SUMMARY The paper extends earlier work on the so-called skew-normal distribution, a family of distributions including the normal, but with an extra parameter to regulate skewness. The present work… Expand