From Gaussian Distribution to Weibull Distribution

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Xu Jiajin
Xu Jiajin
2
Gao Zhentong
Gao Zhentong

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The Gaussian distribution is one of the most widely used statistical distributions, but there are a lot of data that do not conform to Gaussian distribution. For example, structural fatigue life is mostly in accordance with the Weibull distribution rather than the Gaussian distribution, and the Weibull distribution is in a sense a more general full state distribution than the Gaussian distribution. However, the biggest obstacle affecting the application of the Weibull distribution is the complexity of the Weibull distribution, especially the estimation of its three parameters is relatively difficult. In order to avoid this difficulty, people used to solve this problem by taking the logarithm to make the data appear to be more consistent with the Gaussian distribution. But in fact, this approach is problematic, because from the physical point of view, the structure of the data has changed and the physical meaning has changed, so it is not appropriate to use logarithmic Gaussian distribution to fit the original data after logarithm. The author thinks that Z.T. Gao method can give the estimation of three parameters of Weibull distribution conveniently, which lays a solid mathematical foundation for Weibull distribution to directly fit the original data.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Xu Jiajin. 2026. \u201cFrom Gaussian Distribution to Weibull Distribution\u201d. Global Journal of Research in Engineering - I: Numerical Methods GJRE-I Volume 23 (GJRE Volume 23 Issue I1): .

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Gaussian distribution - the foundation of statistical research in engineering and data analysis.
Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

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GJRE-I Classification: DDC Code: 519.24 LCC Code: QA273.6
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v1.2

Issue date

April 27, 2023

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English

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The Gaussian distribution is one of the most widely used statistical distributions, but there are a lot of data that do not conform to Gaussian distribution. For example, structural fatigue life is mostly in accordance with the Weibull distribution rather than the Gaussian distribution, and the Weibull distribution is in a sense a more general full state distribution than the Gaussian distribution. However, the biggest obstacle affecting the application of the Weibull distribution is the complexity of the Weibull distribution, especially the estimation of its three parameters is relatively difficult. In order to avoid this difficulty, people used to solve this problem by taking the logarithm to make the data appear to be more consistent with the Gaussian distribution. But in fact, this approach is problematic, because from the physical point of view, the structure of the data has changed and the physical meaning has changed, so it is not appropriate to use logarithmic Gaussian distribution to fit the original data after logarithm. The author thinks that Z.T. Gao method can give the estimation of three parameters of Weibull distribution conveniently, which lays a solid mathematical foundation for Weibull distribution to directly fit the original data.

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From Gaussian Distribution to Weibull Distribution

Xu Jiajin
Xu Jiajin
Gao Zhentong
Gao Zhentong

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