Renewed empirical formulas for estimating Weibull distribution parameters

The empirical formulas proposed in the literature for estimating the parameters of a two-parameter Weibull distribution, obtained using the equations of the moment method, are considered. It is noted that the formulas used to estimate the shape parameter take the form of various types of dependences...

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Main Author: D.G. Asatryan
Format: Article
Language:English
Published: Samara National Research University 2025-02-01
Series:Компьютерная оптика
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Online Access:https://computeroptics.ru/KO/Annot/KO49-1/490115.html
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author D.G. Asatryan
author_facet D.G. Asatryan
author_sort D.G. Asatryan
collection DOAJ
description The empirical formulas proposed in the literature for estimating the parameters of a two-parameter Weibull distribution, obtained using the equations of the moment method, are considered. It is noted that the formulas used to estimate the shape parameter take the form of various types of dependences on the coefficient of variation of the distribution. By modeling the empirical formulas selected for analysis, a comparative analysis of their errors relative to accurate numerical solutions of the moment method equations was carried out. A renewed empirical formula for the shape parameter is proposed. An approach to estimating the scale parameter is proposed, in which the empirical formula of the latter is reduced to the product of the standard deviation of the distribution by a power function of the coefficient of variation with an exponent equal to – 1.027. The results of applying the updated empirical formulas to numerical data obtained by modeling a random sample from the Weibull distribution are presented. It is shown that the accuracy of the proposed empirical formulas is quite high.
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record_format Article
series Компьютерная оптика
spelling doaj-art-b1da6dae432545e3adb6297a2e68aace2025-08-20T05:51:52ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792025-02-0149112112410.18287/2412-6179-CO-1475Renewed empirical formulas for estimating Weibull distribution parametersD.G. Asatryan0Institute for Informatics and Automation Problems of NAS RA; Russian-Armenian UniversityThe empirical formulas proposed in the literature for estimating the parameters of a two-parameter Weibull distribution, obtained using the equations of the moment method, are considered. It is noted that the formulas used to estimate the shape parameter take the form of various types of dependences on the coefficient of variation of the distribution. By modeling the empirical formulas selected for analysis, a comparative analysis of their errors relative to accurate numerical solutions of the moment method equations was carried out. A renewed empirical formula for the shape parameter is proposed. An approach to estimating the scale parameter is proposed, in which the empirical formula of the latter is reduced to the product of the standard deviation of the distribution by a power function of the coefficient of variation with an exponent equal to – 1.027. The results of applying the updated empirical formulas to numerical data obtained by modeling a random sample from the Weibull distribution are presented. It is shown that the accuracy of the proposed empirical formulas is quite high.https://computeroptics.ru/KO/Annot/KO49-1/490115.htmlweibull distributionshape parameterscale parametercoefficient of variationempirical formulaaccuracy
spellingShingle D.G. Asatryan
Renewed empirical formulas for estimating Weibull distribution parameters
Компьютерная оптика
weibull distribution
shape parameter
scale parameter
coefficient of variation
empirical formula
accuracy
title Renewed empirical formulas for estimating Weibull distribution parameters
title_full Renewed empirical formulas for estimating Weibull distribution parameters
title_fullStr Renewed empirical formulas for estimating Weibull distribution parameters
title_full_unstemmed Renewed empirical formulas for estimating Weibull distribution parameters
title_short Renewed empirical formulas for estimating Weibull distribution parameters
title_sort renewed empirical formulas for estimating weibull distribution parameters
topic weibull distribution
shape parameter
scale parameter
coefficient of variation
empirical formula
accuracy
url https://computeroptics.ru/KO/Annot/KO49-1/490115.html
work_keys_str_mv AT dgasatryan renewedempiricalformulasforestimatingweibulldistributionparameters