Grey-based approach for estimating Weibull model and its application

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Communications in Statistics - Theory and Methods Pub Date : 2023-11-02 DOI:10.1080/03610926.2022.2050397

Xiaomei Liu, Naiming Xie

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引用次数: 2

Abstract

Abstract Weibull distribution is widely used in engineering because of its flexibility to take on many different shapes. For different application fields, people put forward different estimation methods, including grey estimation method. The purpose of this paper is to improve the existing grey estimation method of Weibull distribution as its some serious shortcomings. Firstly, a grey three-parameter Weibull model is proposed in a discrete form. Then, by means of the grey Weibull model, a two-stage hybrid method for estimating the three-parameter Weibull distribution is proposed, which is composed of the linear and nonlinear least square principles. To demonstrate the feasibility of the proposed grey Weibull model, a simulation study was conducted and compared the results with the modified MLE method, and a comparison study on the frequency analysis of four breakdown data sets of epoxy resins is also carried out. Moreover, as a practical application, Weibull model based on the grey estimation approach is applied to the frequency analysis of monthly wind speed of Hohhot in 2018, and compared with a series of existing estimation methods. Results show that the proposed grey Weibull estimation improves the existing grey estimation and can be well applied to the frequency analysis of Weibull data.

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基于灰色的威布尔模型估计方法及其应用

摘要威布尔分布以其可灵活地取多种形状而在工程中得到了广泛的应用。针对不同的应用领域，人们提出了不同的估计方法，其中包括灰色估计方法。本文的目的是改进现有威布尔分布灰色估计方法存在的严重缺陷。首先，提出了一种离散形式的灰色三参数威布尔模型。然后，利用灰色威布尔模型，提出了一种结合线性和非线性最小二乘原理的两阶段混合估计三参数威布尔分布的方法。为了证明所提出的灰色威布尔模型的可行性，进行了仿真研究，并将结果与改进的MLE方法进行了比较，并对环氧树脂四种击穿数据集的频率分析进行了对比研究。此外，作为实际应用，将基于灰色估计方法的威布尔模型应用于2018年呼和浩特市月风速的频率分析，并与现有的一系列估计方法进行比较。结果表明，所提出的灰色威布尔估计改进了现有的灰色估计，可以很好地应用于威布尔数据的频率分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Statistics - Theory and Methods 数学-统计学与概率论

CiteScore

2.00

自引率

12.50%

发文量

320

审稿时长

7.5 months

期刊介绍： The Theory and Methods series intends to publish papers that make theoretical and methodological advances in Probability and Statistics. New applications of statistical and probabilistic methods will also be considered for publication. In addition, special issues dedicated to a specific topic of current interest will also be published in this series periodically, providing an exhaustive and up-to-date review of that topic to the readership.