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 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 Asymptotic curved normal distribution

2019 ◽  
Vol 52 (2) ◽  
pp. 173-186
Author(s):  
C. SATHEESH KUMAR ◽  
G. V. ANILA
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Simulation Study ◽  
Real Life ◽  
Skew Normal Distribution ◽  
Data Set ◽  
New Class ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood

Here we introduce a new class of skew normal distribution as a generalization of the extended skew curved normal distribution of Kumar and Anusree (J. Statist. Res., 2017) and investigate some of its important statistical properties. The location-scale extension of the proposed class of distribution is also defined and discussed the estimation of its parameters by method of maximum likelihood. Further, a real life data set is considered for illustrating the usefulness of the model and a brief simulation study is attempted for assessing the performance of the estimators.

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 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.

scholarly journals Properties and Applications of a New Family of Skew Distributions

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 87
Author(s):  
Emilio Gómez-Déniz ◽  
Barry C. Arnold ◽  
José M. Sarabia ◽  
Héctor W. Gómez
Keyword(s):  
Normal Distribution ◽  
Continuous Distribution ◽  
Central Moment ◽  
Distribution Functions ◽  
Logistic Distribution ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Closed Expression ◽  
Parent Distribution ◽  
Skew Normal

We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals in the statistical literature. The density functions of these new families are given by a closed expression which allows us to easily compute probabilities, moments and related quantities. The second family can exhibit bimodality and its standardized fourth central moment (kurtosis) can be lower than that of the Azzalini skew normal distribution. Since the second proposed family can be bimodal we fit two well-known data set with this feature as applications. We concentrate attention on the case in which the normal distribution is the parent distribution but some consideration is given to other parent distributions, such as the logistic distribution.

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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