Proportional Odds Model Affiliate with Random-Effect Longitudinal Model

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Chin Wan Yoke ◽  
Zarina Mohd Khalid
Keyword(s):  
Longitudinal Analysis ◽  
Proportional Hazards ◽  
Random Effect ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Joint Model ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Proportional Odds ◽  
Longitudinal Measurements

Joint survival-longitudinal analysis gains popularity in recent clinical studies. A proportional hazards (PH) model in survival sub-model is commonly an alternative path to simplify a complex covariates hazard model into a regression model. The PH model however closed only to the Weibull distribution, brought about inappropriate application for the log-logistic observations. Proportional odds (PO) model in that case raised forward to perform similarly with the PH model. The subsequent modelling study is therefore producing a joint PO-longitudinal analysis rather than a widely applicable joint PH-longitudinal analysis. Latent parameters is introduced as a linkage technique between the two sub-models. Investigation in this study relies on the simulation statistics in which the survival time-to-event data and longitudinal measurements are both influenced by a covariate effects. The repeatedly measures data additionally allow for different kind of missingness mechanisms. Maximum likelihood estimation method is applied to the joint model parameters estimation. The performance of the joint model and separated sub-models are then be compared. The illustrated results contributed better estimators on the joint model instead of separated model.

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.

A Space Time Autoaggressive Method Based on Parameters Estimation for Airborne MIMO Radar

2014 ◽  
Vol 556-562 ◽  
pp. 4496-4500
Author(s):  
Xing Hui Chen ◽  
Shi Qiao Gao
Keyword(s):  
Estimation Method ◽  
Mimo Radar ◽  
Space Time ◽  
Parameters Estimation ◽  
Ar Model ◽  
Model Parameters ◽  
Clutter Suppression ◽  
Training Samples ◽  
Multiple Input ◽  
Space Time Adaptive Processing

The clutter distribution of an airborne multiple input and multiple output (MIMO) radar in non-homogeneous environment varies with ranges and samples in different range gates are not independent identically distributed vectors, so that the statistical space time adaptive processing (STAP) methods degrade heavily. A clutter suppression method for airborne MIMO radar in non-homogeneous environments is studied in this paper. Firstly, Space time autoaggressive (STAR) method is introduced to airborne MIMO radar for clutter suppression and then an AR model parameters estimation method for STAR is proposed to decrease the complexity of traditional method. Simulation results show the proposed method can estimate parameters exactly and rapidly with only few training samples and be fit for clutter suppression in non-homogeneous environments.

scholarly journals Parameter Estimation of a Reliability Model of Demand-Caused and Standby-Related Failures of Safety Components Exposed to Degradation by Demand Stress and Ageing That Undergo Imperfect Maintenance

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
S. Martorell ◽  
P. Martorell ◽  
A. I. Sánchez ◽  
R. Mullor ◽  
I. Martón
Keyword(s):  
Parameter Estimation ◽  
Nuclear Power ◽  
Likelihood Estimation ◽  
Real Data ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Reliability Model ◽  
Imperfect Maintenance ◽  
Maintenance Policies

One can find many reliability, availability, and maintainability (RAM) models proposed in the literature. However, such models become more complex day after day, as there is an attempt to capture equipment performance in a more realistic way, such as, explicitly addressing the effect of component ageing and degradation, surveillance activities, and corrective and preventive maintenance policies. Then, there is a need to fit the best model to real data by estimating the model parameters using an appropriate tool. This problem is not easy to solve in some cases since the number of parameters is large and the available data is scarce. This paper considers two main failure models commonly adopted to represent the probability of failure on demand (PFD) of safety equipment: (1) by demand-caused and (2) standby-related failures. It proposes a maximum likelihood estimation (MLE) approach for parameter estimation of a reliability model of demand-caused and standby-related failures of safety components exposed to degradation by demand stress and ageing that undergo imperfect maintenance. The case study considers real failure, test, and maintenance data for a typical motor-operated valve in a nuclear power plant. The results of the parameters estimation and the adoption of the best model are discussed.

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.

scholarly journals Research and application of parameter estimation method in hydrological model based on dual ensemble Kalman filter

2021 ◽  
Author(s):  
Mengtian Lu ◽  
Sicheng Lu ◽  
Weihong Liao ◽  
Xiaohui Lei ◽  
Zhaokai Yin ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Assimilation Efficiency ◽  
Estimation Method ◽  
Initial Distribution ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Multiple Parameters ◽  
Basin Surface

Abstract Although field measurements and using long hydrological datasets provide a reliable method for parameters' calibration, changes in the underlying basin surface and lack of hydrometeorological data may affect parameter accuracy in streamflow simulation. The ensemble Kalman filter (EnKF) can be used as a real-time parameter correction method to solve this problem. In this study, five representative Xin'anjiang model parameters are selected to study the effects of the initial parameter ensemble distribution and the specific function form of the parameter on EnKF parameter estimation process for both single and multiple parameters. Results indicate: (1) the method of parameter calibration to determine the initial distribution mean can improve the assimilation efficiency; (2) there is mutual interference among the parameters during multiple parameters' estimation which invalidates some conclusions of single-parameter estimation. We applied and evaluated the EnKF method in Jinjiang River Basin, China. Compared to traditional approaches, our method showed a better performance in both basins with long hydrometeorological dataset (an increase of Kling–Gupta efficiency (KGE) from 0.810 to 0.887 and a decrease of bias from −1.08% to −0.74%); and in basins with a lack of hydrometeorological data (an increase of KGE from 0.536 to 0.849 and a decrease of bias from −15.55% to −11.42%).

scholarly journals Remaining useful life prediction of cylinder liner based on nonlinear degradation model

2021 ◽  
Vol 24 (1) ◽  
pp. 62-69
Author(s):  
Jianxiong Kang ◽  
Yanjun Lu ◽  
Bin Zhao ◽  
Hongbo Luo ◽  
Jiacheng Meng ◽  
...  
Keyword(s):  
Estimation Method ◽  
Cylinder Liner ◽  
Likelihood Estimation ◽  
Remaining Useful Life ◽  
Model Parameters ◽  
Operational Environment ◽  
Unknown Parameters ◽  
Degradation Model ◽  
Proposed Model ◽  
Useful Life

In order to effectively monitor the wear and predict the life of cylinder liner, a nonlinear degradation model with multi-source uncertainty based on Wiener process is established to evaluate the remaining useful life (RUL) of cylinder liner wear. Due to complex service performance of cylinder liner, the uncertainty of operational environment and working conditions of cylinder liner wear are considered into the model by a random function. The probability density function (PDF) formula of RUL is derived, and the maximum likelihood estimation method is adopted to estimate the unknown parameters of PDF. Considering the evaluated parameters as the initial values, the model parameters are updated adaptively, and an adaptive PDF is obtained. Furthermore, the proposed model is compared with two classical degradation models. The results show that the proposed model has a good performance for predicting the life, and the error is within 5%. The method can provide a reference for condition monitoring of cylinder liner wear.

scholarly journals Odd Lindley-Lomax Model: Statistical Properties and Applications

1970 ◽  
pp. 419-430
Author(s):  
M. Masoom Ali ◽  
Mustafa Ç. Korkmaz ◽  
Haitham M. Yousof ◽  
Nadeem Shafique Butt
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Good Alternative ◽  
Model Parameters ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Computational Aspects ◽  
Maximum Likelihood Estimation Method ◽  
Better Than

 In this work, we focus on some new theoretical and computational aspects of the Odd Lindley-Lomax model. The maximum likelihood estimation method is used to estimate the model parameters. We show empirically the importance and flexibility of the new model in modeling two types of aircraft windshield lifetime data. This model is much better than exponentiated Lomax, gamma Lomax, beta Lomax and Lomax models so the Odd Lindley-Lomax lifetime model is a good alternative to these models in modeling aircraft windshield data. A Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators. 

Motion Model Parameters Estimation for Electronic Image Stabilization Instrument

2013 ◽  
Vol 325-326 ◽  
pp. 1543-1546
Author(s):  
Xun Yu Zhong ◽  
Tian Hui Ren
Keyword(s):  
Motion Estimation ◽  
Least Squares Method ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Block Matching ◽  
Parameters Estimation ◽  
Transformation Model ◽  
Image Motion ◽  
Model Parameters ◽  
Image Stabilization

Fast and optimal motion estimation method is proposed for electronic image stabilization. First, an approach for macro-block judgment is presented. Before motion vectors calculation, gradient information is analyzed, only useful reference blocks that are indispensable for accurate motion estimation are selected, by which the number of macro-blocks for subsequent calculation is reduced. Second, in the block matching, an improved SSDA is used to reduce computing cost. Finally, the affine transformation model and similarity transformation model of image motion are created and using least squares method for solving the optimal estimation of model parameters. Experimental results show the accuracy and fast computing speed of the proposed method.

scholarly journals A New Parametric Life Family of Distributions: Properties, Copula and Modeling Failure and Service Times

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1462
Author(s):  
Mansour Shrahili ◽  
Naif Alotaibi
Keyword(s):  
Maximum Likelihood ◽  
Probability Distributions ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
New Family ◽  
Renyi’S Entropy

A new family of probability distributions is defined and applied for modeling symmetric real-life datasets. Some new bivariate type G families using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. Moreover, some of its statistical properties are presented and studied. Next, the maximum likelihood estimation method is used. A graphical assessment based on biases and mean squared errors is introduced. Based on this assessment, the maximum likelihood method performs well and can be used for estimating the model parameters. Finally, two symmetric real-life applications to illustrate the importance and flexibility of the new family are proposed. The symmetricity of the real data is proved nonparametrically using the kernel density estimation method.

scholarly journals A Study of Convolution Models for Background Correction of BeadArrays

2016 ◽  
Vol 45 (2) ◽  
pp. 15-33
Author(s):  
Rohmatul Fajriyah
Keyword(s):  
Probability Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Parameters Estimation ◽  
Background Correction ◽  
Data Sets ◽  
Normal Model ◽  
Data Set ◽  
Convolution Model ◽  
Maximum Likelihood Estimation Method

The robust multi-array average (RMA), since its introduction in Irizarry, Bolstad,Collin, Cope, Hobbs, and Speed (2003a); Irizarry, Hobbs, Collin, Beazer-Barclay, An-tonellis, Scherf, and Speed (2003b); Irizarry, Wu, and Jaee (2006), has gained popularityamong bioinformaticians. It has evolved from the exponential-normal convolution to thegamma-normal convolution, from single to two channels and from the Aymetrix to theIllumina platform.The Illumina design provides two probe types: the regular and the control probes.This design is very suitable for studying the probability distribution of both and one canapply a convolution model to compute the true intensity estimator.In this paper, we study the existing convolution models for background correction ofIllumina BeadArrays in the literature and give a new estimator for the true intensity,assuming that the intensity value is exponentially or gamma distributed and the noise haslognormal distribution.Our study shows that one of our proposed models, the gamma-lognormal with themethod of moments for parameters estimation, is the optimal one for the benchmark-ing data set with benchmarking criteria, while the gamma-normal model has the bestperformance for the benchmarking data set with simulation criteria.For the publicly available data sets, the gamma-normal and the exponential-gammamodels with maximum likelihood estimation method can not be used and our proposedmodels exponential-lognormal and gamma-lognormal have the best performance, showinga moderate error in background correction and in the parametrization.

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