scholarly journals Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 810
Author(s):  
Tzong-Ru Tsai ◽  
Yuhlong Lio ◽  
Hua Xin ◽  
Hoang Pham
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Survival Function ◽  
Estimation Method ◽  
Mixture Distribution ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Burr Type Xii

Considering the impact of the heterogeneous conditions of the mixture baseline distribution on the parameter estimation of a composite dynamical system (CDS), we propose an approach to infer the model parameters and baseline survival function of CDS using the maximum likelihood estimation and Bayesian estimation methods. The power-trend hazard rate function and Burr type XII mixture distribution as the baseline distribution are used to characterize the changes of the residual lifetime distribution of surviving components. The Markov chain Monte Carlo approach via using a new Metropolis–Hastings within the Gibbs sampling algorithm is proposed to overcome the computation complexity when obtaining the Bayes estimates of model parameters. A numerical example is generated from the proposed CDS to analyze the proposed procedure. Monte Carlo simulations are conducted to investigate the performance of the proposed methods, and results show that the proposed Bayesian estimation method outperforms the maximum likelihood estimation method to obtain reliable estimates of the model parameters and baseline survival function in terms of the bias and mean square error.

Hybrid Genetic Algorithm: A Robust Parameter Estimation Technique and Its Application to Heavy Duty Vehicles

2003 ◽  
Author(s):  
Jie Xiao ◽  
Bohdan Kulakowski
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hybrid Genetic Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Optimization Techniques ◽  
Estimation Technique ◽  
Estimation Strategy ◽  
Analysis Experiment

This study aims at establishing an accurate yet efficient parameter estimation strategy for developing dynamic vehicle models that can be easily implemented for simulation and controller design purposes. Generally, conventional techniques such as Least Square Estimation (LSE), Maximum Likelihood Estimation (MLE), and Instrumental Variable Methods (IVM), can deliver sufficient estimation results for given models that are linear-in-the-parameter. However, many identification problems in the engineering world are very complex in nature and are quite difficult to solve by those techniques. For the nonlinear-in-the-parameter models, it is almost impossible to find an analytical solution. As a result, numerical algorithms have to be used in calculating the estimates. In the area of model parameter estimation for motor vehicles, most studies performed so far have been limited either to the linear-in-the-parameter models, or in their ability to handle multi-modal error surfaces. For models with nondifferentiable cost functions, the conventional methods will not be able to locate the optimal estimates of the unknown parameters. This concern naturally leads to the exploration of other search techniques. In particular, Genetic Algorithms (GAs), as population-based global optimization techniques that emulate natural genetic operators, have been introduced into the field of parameter estimation. In this paper, hybrid parameter estimation technique is developed to improve computational efficiency and accuracy of pure GA-based estimation. The proposed strategy integrates a GA and the Maximum Likelihood Estimation. Choices of input signals and estimation criterion are discussed involving an extensive sensitivity analysis. Experiment-related aspects, such as imperfection of data acquisition, are also considered. Computer simulation results reveal that the hybrid parameter estimation method proposed in this study shows great potential to outperform conventional techniques and pure GAs in accuracy, efficiency, as well as robustness with respect to the initial guesses and measurement uncertainty. Primary experimental validation is also implemented including interpretation and processing of field test data, as well as analysis of errors associated with aspects of experiment design. To provide more guidelines for implementing the hybrid GA approach, some practical guidelines on application of the proposed parameter estimation strategy are discussed.

scholarly journals Estimation of 2- and 3-parameter BURR type XII distribution using EM algorithm

2014 ◽  
Vol 10 (2) ◽  
Author(s):  
Nor Hidayah Ismail ◽  
Zarina Mohd Khalid
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Censored Data ◽  
Simulation Study ◽  
Expectation Maximization ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Gamma Distributions ◽  
Burr Type Xii

The Burr Type XII distribution is one of the systems of continuous distributions and is widely known because the distribution includes the characteristics of various well known distributions such as Weibull and gamma distributions. Maximum likelihood estimation (MLE) has been a common method in estimating model parameters. In this paper, we present an alternative method that is expectation-maximization (EM) algorithm to estimate the two- and three- parameter Burr Type XII distributions in the presence of complete and censored data. Furthermore, simulation study is conducted to compare the efficiency and accuracy of MLE and EM algorithm. We discover that EM estimation is more efficient and accurate than those estimates obtained via MLE approach.________________________________________GRAPHICAL ABSTRACT

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals A Bi-Level Weibull Model with Applications to Two Ordered Events

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Shuguang Song ◽  
Hanlin Liu ◽  
Mimi Zhang ◽  
Min Xie
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Mixture Distribution ◽  
Likelihood Estimation ◽  
Random Variable ◽  
Weibull Model ◽  
Reliability Function ◽  
The Other ◽  
Regularity Conditions ◽  
Maximum Likelihood Estimation Method

In this paper, we propose and study a new bivariate Weibull model, called Bi-levelWeibullModel, which arises when one failure occurs after the other. Under some specific regularity conditions, the reliability function of the second event can be above the reliability function of the first event, and is always above the reliability function of the transformed first event, which is a univariate Weibull random variable. This model is motivated by a common physical feature that arises fromseveral real applications. The two marginal distributions are a Weibull distribution and a generalized three-parameter Weibull mixture distribution. Some useful properties of the model are derived, and we also present the maximum likelihood estimation method. A real example is provided to illustrate the application of the model.

scholarly journals Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes

2006 ◽  
Vol 3 (4) ◽  
pp. 1603-1627 ◽  
Author(s):  
W. Wang ◽  
P. H. A. J. M. van Gelder ◽  
J. K. Vrijling ◽  
X. Chen
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Long Memory ◽  
Positive Relationship ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Large Data ◽  
Daily Streamflow ◽  
Maximum Likelihood Estimation Method

Abstract. The Lo's R/S tests (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and the maximum likelihood estimation method implemented in S-Plus (S-MLE) are evaluated through intensive Mote Carlo simulations for detecting the existence of long-memory. It is shown that, it is difficult to find an appropriate lag q for Lo's test for different AR and ARFIMA processes, which makes the use of Lo's test very tricky. In general, the GPH test outperforms the Lo's test, but for cases where there is strong autocorrelations (e.g., AR(1) processes with φ=0.97 or even 0.99), the GPH test is totally useless, even for time series of large data size. Although S-MLE method does not provide a statistic test for the existence of long-memory, the estimates of d given by S-MLE seems to give a good indication of whether or not the long-memory is present. Data size has a significant impact on the power of all the three methods. Generally, the power of Lo's test and GPH test increases with the increase of data size, and the estimates of d with GPH test and S-MLE converge with the increase of data size. According to the results with the Lo's R/S test (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and the S-MLE method, all daily flow series exhibit long-memory. The intensity of long-memory in daily streamflow processes has only a very weak positive relationship with the scale of watershed.

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