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366570

A Proposed Distribution-Free Test For Symmetry of Grouped Data

Article

Last updated: 05 Jan 2025

Subjects

-

Tags

Applied Statistics and Econometrics
Mathematical Statistics

Abstract

This paper introduces a new, straightforward test for analyzing the symmetry of data represented in frequency distributions. Unlike other methods, this test doesn't require any assumptions about the underlying statistical distribution of the data. The only prerequisite is that the data has equal-sized categories (bins) and none of these categories have a frequency of zero. This makes the test both statistically robust and computationally efficient. In simpler terms, the test offers a user-friendly way to assess whether a data set leans towards one side or the other (positive or negative skew) without relying on specific statistical models. The test relies on a statistic denoted by G, which was introduced by \cite{Eltehiwy}. We introduce and study the properties of G statistic and obtain its mean and variance. We explore the Asymptotic distribution of the G Statistic. Finally, a worked example and a practical example is presented to illustrate how the test is implemented.

DOI

10.21608/cjmss.2024.288527.1052

Keywords

Asymptotic normal distribution, Distribution-Free Test, skewness, Symmetry

Authors

First Name

Mahmoud

Last Name

Eltehiwy

MiddleName

-

Affiliation

statistics department, the Politics and Economics faculty, Beni -Suef university, Egypt

Email

mahmoudtehiwy@gmail.com

City

-

Orcid

-

First Name

Abu Bakr

Last Name

Abdul-Motaal

MiddleName

-

Affiliation

Faculty of Commerce, Department of Statistics, South Valley University, Egypt.

Email

abubakrabdulmotaal@gmail.com

City

-

Orcid

-

Volume

3

Article Issue

2

Related Issue

47327

Issue Date

2024-11-01

Receive Date

2024-05-10

Publish Date

2024-11-01

Page Start

417

Page End

431

Print ISSN

2974-3435

Online ISSN

2974-3443

Link

https://cjmss.journals.ekb.eg/article_366570.html

Detail API

https://cjmss.journals.ekb.eg/service?article_code=366570

Order

366,570

Type

Original Article

Type Code

2,545

Publication Type

Journal

Publication Title

Computational Journal of Mathematical and Statistical Sciences

Publication Link

https://cjmss.journals.ekb.eg/

MainTitle

A Proposed Distribution-Free Test For Symmetry of Grouped Data

Details

Type

Article

Created At

29 Dec 2024