Point Estimation of the Location Parameter of a Skew-Normal Distribution: Some Fixed Sample and Asymptotic Results

2019 ◽  
Vol 13 (2) ◽  
Author(s):  
Phontita Thiuthad ◽  
Nabendu Pal
Keyword(s):  
Normal Distribution ◽  
Location Parameter ◽  
Point Estimation ◽  
Skew Normal Distribution ◽  
Asymptotic Results ◽  
Fixed Sample ◽  
Skew Normal

scholarly journals A New Extended Mixture Skew Normal Distribution, With Applications

2019 ◽  
Vol 42 (2) ◽  
pp. 167-183
Author(s):  
Haroon M. Barakat ◽  
Abdallh W. Aboutahoun ◽  
Naeema El-kadar
Keyword(s):  
Normal Distribution ◽  
Location Parameter ◽  
Distribution Functions ◽  
Maximum Likelihood Estimates ◽  
Computational Techniques ◽  
Model Parameters ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Wide Range ◽  
Skew Normal

One of the most important property of the mixture normal distributions-model is its flexibility to accommodate various types of distribution functions (df's). We show that the mixture of the skew normal distribution and its reverse, after adding a location parameter to the skew normal distribution, and adding the same location parameter with different sign to its reverse is a family of df's that contains all the possible types of df's. Besides, it has a very remarkable wide range of the indices of skewness and kurtosis. Computational techniques using EM-type algorithms are employed for iteratively computing maximum likelihood estimates of the model parameters. Moreover, an application with a body mass index real data set is presented.

scholarly journals Hypothesis Testing on the Location Parameter of a Skew-Normal Distribution (SND) with Application

2018 ◽  
Vol 20 ◽  
pp. 03003
Author(s):  
Phontita Thiuthad ◽  
Nabendu Pal
Keyword(s):  
Normal Distribution ◽  
Real Life ◽  
Location Parameter ◽  
Test Methods ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Sample Mean ◽  
Real Life Data ◽  
Approximate Probability ◽  
Skew Normal

This work deals with testing a hypothesis on the location parameter (μ) of a skew-normal distribution (SND) based on a random sample of size n. The details of this work can be summarized in four major components: (a) First we review some useful results on SND, including the approximate probability distribution of the sample average. (b) Next, we develop several tests to test a hypothesis on μ based on the sample mean when the scale (σ) and shape (λ) parameters are known. (c) The tests for the known scale and shape are then extended for unknown scale and shape. (d) Finally, the test methods have been used for a real-life data set.

scholarly journals Bayesian Inference of Finite Population Quantiles for Skewed Survey Data Using Skew-Normal Penalized Spline Regression

2019 ◽  
Vol 8 (4) ◽  
pp. 792-816
Author(s):  
Yutao Liu ◽  
Qixuan Chen
Keyword(s):  
Normal Distribution ◽  
Survey Data ◽  
Finite Population ◽  
Location Parameter ◽  
Penalized Splines ◽  
Sample Survey ◽  
Skew Normal Distribution ◽  
Scale Parameters ◽  
Penalized Spline ◽  
Skew Normal

Abstract Skewed data are common in sample surveys. In probability proportional to size sampling, we propose two Bayesian model-based predictive methods for estimating finite population quantiles with skewed sample survey data. We assume the survey outcome to follow a skew-normal distribution given the probability of selection and model the location and scale parameters of the skew-normal distribution as functions of the probability of selection. To allow a flexible association between the survey outcome and the probability of selection, the first method models the location parameter with a penalized spline and the scale parameter with a polynomial function, while the second method models both the location and scale parameters with penalized splines. Using a fully Bayesian approach, we obtain the posterior predictive distributions of the nonsampled units in the population and thus the posterior distributions of the finite population quantiles. We show through simulations that our proposed methods are more efficient and yield shorter credible intervals with better coverage rates than the conventional weighted method in estimating finite population quantiles. We demonstrate the application of our proposed methods using data from the 2013 National Drug Abuse Treatment System Survey.

EM algorithm using overparameterization for the multivariate skew-normal distribution

2021 ◽  
Author(s):  
Toshihiro Abe ◽  
Hironori Fujisawa ◽  
Takayuki Kawashima ◽  
Christophe Ley
Keyword(s):  
Em Algorithm ◽  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Skew Normal

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.

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

Symmetry ◽  
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.

The additive logistic skew-normal distribution on the simplex

2005 ◽  
Vol 19 (3) ◽  
pp. 205-214 ◽  
Author(s):  
G. Mateu-Figueras ◽  
V. Pawlowsky-Glahn ◽  
C. Barceló-Vidal
Keyword(s):  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Skew Normal

On Some Properties of the Unified Skew Normal Distribution

2013 ◽  
Vol 7 (3) ◽  
pp. 480-495 ◽  
Author(s):  
Arjun K. Gupta ◽  
Mohammad A. Aziz ◽  
Wei Ning
Keyword(s):  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Unified Skew Normal Distribution ◽  
Skew Normal
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