scholarly journals Saddlepoint approximation for distribution function of sample mean of skew-normal distribution

2013 ◽  
Vol 24 (6) ◽  
pp. 1211-1219 ◽  
Author(s):  
Jong-Hwa Na ◽  
Hye-Kyung Yu
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Saddlepoint Approximation ◽  
Skew Normal Distribution ◽  
Sample Mean ◽  
Skew Normal

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.

Saddlepoint approximations for bivariate distributions

1990 ◽  
Vol 27 (03) ◽  
pp. 586-597 ◽  
Author(s):  
Suojin Wang
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Normal Distribution ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
Monte Carlo Study ◽  
Cumulative Distribution ◽  
Normal Distribution Function ◽  
Sample Mean ◽  
Saddlepoint Approximations

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

Saddlepoint approximations for bivariate distributions

1990 ◽  
Vol 27 (3) ◽  
pp. 586-597 ◽  
Author(s):  
Suojin Wang
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Normal Distribution ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
Monte Carlo Study ◽  
Cumulative Distribution ◽  
Normal Distribution Function ◽  
Sample Mean ◽  
Saddlepoint Approximations

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

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 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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