Histogram Filter with Adjustment of the Smoothing Parameter Based on The Minimization of the Chi-Square Test

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Ausiannikau Andrei V
Ausiannikau Andrei V

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GJRE Volume 22 Issue J3

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For the formation of adequate models of objects of statistical research, with the possible high cost of a measuring experiment or the process of obtaining data, fast and “correct” identification (recognition) of the probability distribution density (PDD) based on the construction of simple histogram estimates is required. The requirement for rapid identification can be considered equivalent to having a limited and small amount of data. The article proposes a theoretically substantiated method for constructing a histogram filter (HF), which is a linear combination of the amount of data in adjacent intervals with constant weight coefficients, which can be expressed in terms of a single coefficient k -the smoothing parameter. The estimation of the smoothing coefficient is based on the minimization of the modified chi-square test. The theorem given in the article establishes that the value of the mathematical expectation of the chisquare test, after applying the HF, decreases by k times compared to the standard mathematical expectation of the criterion with a unit inclusion function.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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Not applicable for this article.

Ausiannikau Andrei V. 2026. \u201cHistogram Filter with Adjustment of the Smoothing Parameter Based on The Minimization of the Chi-Square Test\u201d. Global Journal of Research in Engineering - J: General Engineering GJRE-J Volume 22 (GJRE Volume 22 Issue J3): .

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Enhanced algorithm for histogram smoothing in engineering studies.
Journal Specifications

Crossref Journal DOI 10.17406/gjre

Print ISSN 0975-5861

e-ISSN 2249-4596

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GJRE-J Classification: DDC Code: 020.3 LCC Code: Z1006
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v1.2

Issue date

September 12, 2022

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English

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For the formation of adequate models of objects of statistical research, with the possible high cost of a measuring experiment or the process of obtaining data, fast and “correct” identification (recognition) of the probability distribution density (PDD) based on the construction of simple histogram estimates is required. The requirement for rapid identification can be considered equivalent to having a limited and small amount of data. The article proposes a theoretically substantiated method for constructing a histogram filter (HF), which is a linear combination of the amount of data in adjacent intervals with constant weight coefficients, which can be expressed in terms of a single coefficient k -the smoothing parameter. The estimation of the smoothing coefficient is based on the minimization of the modified chi-square test. The theorem given in the article establishes that the value of the mathematical expectation of the chisquare test, after applying the HF, decreases by k times compared to the standard mathematical expectation of the criterion with a unit inclusion function.

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Histogram Filter with Adjustment of the Smoothing Parameter Based on The Minimization of the Chi-Square Test

Ausiannikau Andrei V
Ausiannikau Andrei V

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