A modified goodness-of-fit test based on likelihood ratio for the skew-normal distribution

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 distribution of BMI. Due to the skew and bimodal nature, we focus on modeling BMI with flexible skewed distributions. The distributions are fitted to University of Wisconsin–Eau Claire (UWEC) BMI data and to a data obtained from National Health and Nutrition Survey (NHANES). The model parameters are obtained using maximum likelihood estimation method. We compare flexible models to more conventional distributions, such as skew-normal, and skew-t distributions using AIC and BIC and Kolmogorov-Smirnov (K-S) goodness-of-fit test. Our results indicate that the skew-t and Alpha-Skew-Laplace distributions are reasonably competitive when describing unimodal BMI data whereas Alpha-Skew-Laplace and finite mixture of scale mixture of skew-normal and skew-t distributions are better alternatives to both unimodal and bimodal conventional distributions. The results we obtained are useful because we believe the models discussed in ours study will offer a framework for testing features such as bimodality, asymmetry, and robustness of the BMI data, thus providing a more detailed and accurate understanding of the distribution of BMI. KEYWORDS: Body Mass Index; Skew-normal distribution; Skew-t distribution; Flexible skewed distributions; Mixture distributions; Scale mixture of skew-normal distribution; K-S test

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EM algorithm using overparameterization for the multivariate skew-normal distribution

Econometrics and Statistics ◽

10.1016/j.ecosta.2021.03.003 ◽

2021 ◽

Author(s):

Toshihiro Abe ◽

Hironori Fujisawa ◽

Takayuki Kawashima ◽

Christophe Ley

Keyword(s):

Em Algorithm ◽

Normal Distribution ◽

Skew Normal Distribution ◽

Skew Normal

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Parameter estimation for univariate Skew-Normal distribution based on the modified empirical characteristic function

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2021.1883655 ◽

2021 ◽

pp. 1-12

Author(s):

Gege Hou ◽

Ancha Xu ◽

Fengjing Cai ◽

You-Gan Wang

Keyword(s):

Parameter Estimation ◽

Characteristic Function ◽

Normal Distribution ◽

Empirical Characteristic Function ◽

Skew Normal Distribution ◽

Skew Normal

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Some properties of the unified skew-normal distribution

Statistical Papers ◽

10.1007/s00362-021-01235-2 ◽

2021 ◽

Author(s):

Reinaldo B. Arellano-Valle ◽

Adelchi Azzalini

Keyword(s):

Normal Distribution ◽

Fourth Order ◽

Probability Distributions ◽

Skew Normal Distribution ◽

Present Contribution ◽

The Family ◽

Multivariate Skewness ◽

Unified Skew Normal Distribution ◽

Skewness And Kurtosis ◽

Skew Normal

AbstractFor the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia’s measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.

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Copulaesque Versions of the Skew-Normal and Skew-Student Distributions

Symmetry ◽

10.3390/sym13050815 ◽

2021 ◽

Vol 13 (5) ◽

pp. 815

Author(s):

Christopher Adcock

Keyword(s):

Distribution Function ◽

Normal Distribution ◽

Degrees Of Freedom ◽

Special Functions ◽

Normal Distribution Function ◽

Skew Normal Distribution ◽

Marginal Distributions ◽

Student’S T ◽

Normal Copula ◽

Skew Normal

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples.

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