Maximum likelihood parameter estimation in the extended Weibull distribution and its applications to breakdown voltage estimation

2002 ◽  
Vol 9 (4) ◽  
pp. 524-536 ◽  
Author(s):  
H. Hirose
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Breakdown Voltage ◽  
Extended Weibull Distribution

scholarly journals Reliability-Centered Maintenance: Analyzing Failure in Harvest Sugarcane Machine Using Some Generalizations of the Weibull Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Pedro L. Ramos ◽  
Diego C. Nascimento ◽  
Camila Cocolo ◽  
Márcio J. Nicola ◽  
Carlos Alonso ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Cost Savings ◽  
Maintenance Scheduling ◽  
Predictive Analysis ◽  
Main Interest ◽  
Mathematical Background ◽  
Reliability Centered Maintenance ◽  
Best Fit

We considered five generalizations of the standard Weibull distribution to describe the lifetime of two important components of sugarcane harvesting machines. The harvesters considered in the analysis harvest an average of 20 tons of sugarcane per hour and their malfunction may lead to major losses; therefore, an effective maintenance approach is of main interest for cost savings. For the considered distributions, mathematical background is presented. Maximum likelihood is used for parameter estimation. Further, different discrimination procedures were used to obtain the best fit for each component. At the end, we propose a maintenance scheduling for the components of the harvesters using predictive analysis.

Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

Application of differential evolution for wind speed distribution parameters estimation

2021 ◽  
pp. 0309524X2199996
Author(s):  
Rajesh Kumar ◽  
Arun Kumar
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Wind Speed ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Speed Distribution ◽  
De Algorithm ◽  
Wind Speed Distribution ◽  
Distribution Parameters

Weibull distribution is an extensively used statistical distribution for analyzing wind speed and determining energy potential studies. Estimation of the wind speed distribution parameter is essential as it significantly affects the success of Weibull distribution application to wind energy. Various estimation methods viz. graphical method, moment method (MM), maximum likelihood method (ML), modified maximum likelihood method, and energy pattern factor method or power density method have been presented in various reported research studies for accurate estimation of distribution parameters. ML is the most preferred approach to study the parameter estimation. ML works on the principle of forming a likelihood function and maximizing the function for parameter estimation. ML generally uses the numerical based iterative method, such as Newton–Raphson. However, the iterative methods proposed in the literature are generally computationally intensive. In this paper, an efficient technique utilizing differential evolution (DE) algorithm to enhance the estimation accuracy of maximum likelihood estimation has been presented. The [Formula: see text] of GA-Weibull, SA-Weibull, and DE-Weibull is 0.958, 0.953, and 0.973 respectively, and value of RMSE of DE-Weibull 0.0083, GA-Weibull (0.0104), and SA-Weibull (0.0110), for the yearly wind speed data are obtained. The lowest root mean square error and larger regression value for both monthly and yearly wind speed data indicate that the DE-Weibull distribution has the best goodness of fit and advocate the DE algorithm for the parameter estimation.

scholarly journals Cubic Transformation of Exponential Weibull and its Statistical Properties

2020 ◽  
pp. 39-50
Author(s):  
Haiyue Wang ◽  
Zhenhua Bao
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Statistical Properties ◽  
Reasoning Process ◽  
The Family

In this paper, a cubic transformation exponential Weibull distribution is proposed by using the family of cubic transformation distributions introduced by Rahman et al.The reasoning process of the proposed cubic transformation exponential Weibull distribution is discussed in detail, and its statistical properties and parameter estimation are also discussed.Using real data, the maximum likelihood estimation is used to simulate. Through the comparison of fitting results, it is concluded that the cubic transformation exponential Weibull distribution proposed in this paper has stronger applicability.

Maximum Likelihood Method for Parameter Estimation of Weibull Distribution Model Based on Fruit Fly Optimization Algorithm

2014 ◽  
Vol 602-605 ◽  
pp. 3508-3511 ◽  
Author(s):  
Xiang Ping Meng ◽  
Chuan Qi Zhao ◽  
Lei Huo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Optimization Algorithm ◽  
Likelihood Estimation ◽  
Fruit Fly ◽  
Distribution Model ◽  
Fruit Fly Optimization Algorithm ◽  
Fruit Fly Optimization

It is difficult to estimate the parameters of Weibull distribution model using Maximum Likelihood Estimation based on Ant Colony Algorithm (ACA) or Particle Swarm Optimization theory (PSO) for which is easy to fall into premature and needs more variables, thus Fruit Fly Optimization Algorithm (FOA) theory is introduced into maximum likelihood estimation, and a parameter estimation method based on FOA theory is proposed, an example has been simulated to verify the feasibility and effectiveness of this method by comparing with ACA and PSO.

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