scholarly journals A Family of Skew-Normal Distributions for Modeling Proportions and Rates with Zeros/Ones Excess

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1439
Author(s):  
Guillermo Martínez-Flórez ◽  
Víctor Leiva ◽  
Emilio Gómez-Déniz ◽  
Carolina Marchant
Keyword(s):  
Normal Distribution ◽  
Real Data ◽  
Continuous Variable ◽  
Likelihood Method ◽  
Skew Normal Distribution ◽  
Normal Distributions ◽  
New Type ◽  
Skew Normal Distributions ◽  
Information Matrices ◽  
Skew Normal

In this paper, we consider skew-normal distributions for constructing new a distribution which allows us to model proportions and rates with zero/one inflation as an alternative to the inflated beta distributions. The new distribution is a mixture between a Bernoulli distribution for explaining the zero/one excess and a censored skew-normal distribution for the continuous variable. The maximum likelihood method is used for parameter estimation. Observed and expected Fisher information matrices are derived to conduct likelihood-based inference in this new type skew-normal distribution. Given the flexibility of the new distributions, we are able to show, in real data scenarios, the good performance of our proposal.

scholarly journals Using Iterative Reweighting Algorithm and Genetic Algorithm to Calculate The Estimation of The Parameters Of The Maximum Likelihood of The Skew Normal Distribution

2021 ◽  
Vol 27 (127) ◽  
pp. 253-264
Author(s):  
مرتضى علاء الخفاجي ◽  
رباب عبد الرضا البكري
Keyword(s):  
Genetic Algorithm ◽  
Maximum Likelihood ◽  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Skew Normal Distribution ◽  
Iterative Reweighting ◽  
Non Linear Equation ◽  
Skew Normal

Excessive skewness which occurs sometimes in the data is represented as an obstacle against normal distribution. So, recent studies have witnessed activity in studying the skew-normal distribution (SND) that matches the skewness data which is regarded as a special case of the normal distribution with additional skewness parameter (α), which gives more flexibility to the normal distribution. When estimating the parameters of (SND), we face the problem of the non-linear equation and by using the method of Maximum Likelihood estimation (ML) their solutions will be inaccurate and unreliable. To solve this problem, two methods can be used that are: the genetic algorithm (GA) and the iterative reweighting algorithm (IR) based on the Maximum Likelihood method. Monte Carlo simulation was used with different skewness levels and sample sizes, and the superiority of the results was compared. It was concluded that (SND) model estimation using (GA) is the best when the samples sizes are small and medium, while large samples indicate that the (IR) algorithm is the best. The study was also done using real data to find the parameter estimation and a comparison between the superiority of the results based on (AIC, BIC, Mse and Def) criteria.

scholarly journals On Properties of the Bimodal Skew-Normal Distribution and an Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 703
Author(s):  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco ◽  
Osvaldo Venegas ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Normal Distributions ◽  
Stochastic Representations ◽  
Skew Normal

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.

scholarly journals A Novel Multivariate Generalized Skew-Normal Distribution with Two Parameters BGSNn, m (λ1, λ2)

2014 ◽  
Vol 10 (1) ◽  
pp. 75-79 ◽  
Author(s):  
B. Fathi ◽  
P. Hasanalipour
Keyword(s):  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Normal Distributions ◽  
New Class ◽  
Skew Normal Distributions ◽  
Two Parameters ◽  
Skew Normal

Abstract In this paper we first introduce a new class of multivariate generalized asymmetric skew-normal distributions with two parameters λ1,λ2 that we present it by BGSNn, m (λ1,λ2), and we finally obtain some special properties of BGSNnm(λ1,λ2).

scholarly journals Multivariate Skew-Power-Normal Distributions: Properties and Associated Inference

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1509
Author(s):  
Guillermo Martínez-Flórez ◽  
Artur J. Lemonte ◽  
Hugo S. Salinas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Multivariate Distributions ◽  
Likelihood Approach ◽  
Information Matrices ◽  
Univariate Distribution

The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution, we extend the univariate power-normal distribution to the multivariate setup. Structural properties of the new multivariate distributions are established. We consider the maximum likelihood method to estimate the unknown parameters, and the observed and expected Fisher information matrices are also derived. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes.

scholarly journals Prefeasibility Study of Photovoltaic Power Potential Based on a Skew-Normal Distribution

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 676
Author(s):  
Shin Young Kim ◽  
Benedikt Sapotta ◽  
Gilsoo Jang ◽  
Yong-Heack Kang ◽  
Hyun-Goo Kim
Keyword(s):  
Normal Distribution ◽  
Solar Irradiance ◽  
Information Criterion ◽  
Energy Performance ◽  
Skew Normal Distribution ◽  
Normal Distributions ◽  
Photovoltaic Power ◽  
Natural Energy ◽  
The Difference ◽  
Skew Normal

Solar energy does not always follow the normal distribution due to the characteristics of natural energy. The system advisor model (SAM), a well-known energy performance analysis program, analyzes exceedance probabilities by dividing solar irradiance into two cases, i.e., when normal distribution is followed, and when normal distribution is not followed. However, it does not provide a mathematical model for data distribution when not following the normal distribution. The present study applied the skew-normal distribution when solar irradiance does not follow the normal distribution, and calculated photovoltaic power potential to compare the result with those using the two existing methods. It determined which distribution was more appropriate between normal and skew-normal distributions using the Jarque–Bera test, and then the corrected Akaike information criterion (AICc). As a result, three places in Korea showed that the skew-normal distribution was more appropriate than the normal distribution during the summer and winter seasons. The AICc relative likelihood between two models was more than 0.3, which showed that the difference between the two models was not extremely high. However, considering that the proportion of uncertainty of solar irradiance in photovoltaic projects was 5% to 17%, more accurate models need to be chosen.

scholarly journals Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness

2018 ◽  
Vol 28 (5) ◽  
pp. 1457-1476 ◽  
Author(s):  
Luis M Castro ◽  
Wan-Lun Wang ◽  
Victor H Lachos ◽  
Vanda Inácio de Carvalho ◽  
Cristian L Bayes
Keyword(s):  
Longitudinal Data ◽  
Normal Distribution ◽  
Simulated Data ◽  
Real Data ◽  
Skew Normal Distribution ◽  
Individual Subject ◽  
Bayesian Semiparametric ◽  
Nonlinear Relation ◽  
The Individual ◽  
Skew Normal

In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient’s responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.

scholarly journals The Extended Birnbaum–Saunders Distribution Based on the Scale Shape Mixture of Skew Normal Distributions

2021 ◽  
Vol 20 (4) ◽  
pp. 481-517
Author(s):  
Tahereh Poursadeghfard ◽  
Alireza Nematollahi ◽  
Ahad Jamalizadeh
Keyword(s):  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Parameter Estimates ◽  
Asymptotic Covariance Matrix ◽  
Finite Sample ◽  
Data Set ◽  
Normal Distributions ◽  
Skew Normal Distributions ◽  
Skew Normal

AbstractIn this article, a large class of univriate Birnbaum–Saunders distributions based on the scale shape mixture of skew normal distributions is introduced which generates suitable subclasses for modeling asymmetric data in a variety of settings. The moments and maximum likelihood estimation procedures are disscused via an ECM-algorithm. The observed information matrix to approximate the asymptotic covariance matrix of the parameter estimates is then derived in some subclasses. A simulation study is also performed to evaluate the finite sample properties of ML estimators and finally, a real data set is analyzed for illustrative purposes.

scholarly journals Some properties of the unified skew-normal distribution

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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