AN ANALYSIS OF ACCELERATED PERFORMANCE DEGRADATION TESTS ASSUMING THE ARRHENIUS STRESS-RELATIONSHIP

2008 ◽  
Vol 25 (06) ◽  
pp. 847-864 ◽  
Author(s):  
TAE HYOUNG KANG ◽  
SANG WOOK CHUNG ◽  
WON YOUNG YUN
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Exposure Time ◽  
Failure Time ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Performance Degradation ◽  
Maximum Likelihood Estimates ◽  
Degradation Tests

An analytical model is developed for accelerated performance degradation tests. The performance degradations of products at a specified exposure time are assumed to follow a normal distribution. It is assumed that the relationship between the location parameter of normal distribution and the exposure time is a linear function of the exposure time that the slope coefficient of the linear relationship has an Arrhenius dependence on temperature, and that the scale parameter of the normal distribution is constant and independent of temperature or exposure time. The method of maximum likelihood estimation is used to estimate the parameters involved. The likelihood function for the accelerated performance degradation data is derived. The approximated variance-covariance matrix is also derived for calculating approximated confidence intervals of maximum likelihood estimates. Finally we use two real examples for estimating the failure-time distribution, technically defined as the time when performance degrades below a specified level.

Maximum likelihood estimation in nonlinear structured fisheries models using survey and catch-at-age data

2011 ◽  
Vol 68 (10) ◽  
pp. 1717-1731 ◽  
Author(s):  
Christian N. Brinch ◽  
Anne Maria Eikeset ◽  
Nils Chr. Stenseth
Keyword(s):  
Maximum Likelihood ◽  
Gadus Morhua ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Simulated Maximum Likelihood ◽  
True Parameter ◽  
Bayesian Techniques ◽  
Age Structured ◽  
Parameter Values

Age-structured population dynamics models play an important role in fisheries assessments. Such models have traditionally been estimated using crude likelihood approximations or more recently using Bayesian techniques. We contribute to this literature with three main messages. Firstly, we demonstrate how to estimate such models efficiently by simulated maximum likelihood using Laplace importance samplers for the likelihood function. Secondly, we demonstrate how simulated maximum likelihood estimates may be validated using different importance samplers known to approach the exact likelihood function in different regions of the parameter space. Thirdly, we show that our method works in practice by Monte Carlo simulations using parameter values as estimated from data on the Northeast Arctic cod ( Gadus morhua ) stock. The simulations suggest that we are able to recover the unknown true maximum likelihood estimates using moderate importance sample sizes and show that we are able to adequately recover the true parameter values.

Maximum Likelihood Estimation and Testing of a Poisson Regression Model

1992 ◽  
Vol 31 (03) ◽  
pp. 215-218
Author(s):  
J. Y. Wan ◽  
A. T. Galecki
Keyword(s):  
Maximum Likelihood ◽  
Regression Model ◽  
Poisson Regression ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Incidence Rates ◽  
Maximum Likelihood Estimates ◽  
Categorical Variables ◽  
Poisson Regression Model ◽  
Regression Parameters

Abstract:A Poisson regression model is proposed for the analysis of incidence rates presented in a two-way table classified by two categorical variables. It is shown that the likelihood function is the same as that using Glasser’s exponential covariate model. An algorithm is given to solve the maximum likelihood estimates of the regression parameters. The model is evaluated via deviance and the method is illustrated with an example. Some extensions of the model are discussed.

scholarly journals Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

A HYBRID GENETIC ALGORITHM FOR THE MAXIMUM LIKELIHOOD ESTIMATION OF MODELS WITH MULTIPLE EQUILIBRIA: A FIRST REPORT

2005 ◽  
Vol 01 (02) ◽  
pp. 295-303 ◽  
Author(s):  
VICTOR AGUIRREGABIRIA ◽  
PEDRO MIRA
Keyword(s):  
Genetic Algorithm ◽  
Maximum Likelihood ◽  
Multiple Equilibria ◽  
Structural Parameters ◽  
Hybrid Genetic Algorithm ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Large Space ◽  
Pseudo Maximum Likelihood ◽  
Structural Econometric

This paper presents a hybrid genetic algorithm to obtain maximum likelihood estimates of parameters in structural econometric models with multiple equilibria. The algorithm combines a pseudo maximum likelihood (PML) procedure with a genetic algorithm (GA). The GA searches globally over the large space of possible combinations of multiple equilibria in the data. The PML procedure avoids the computation of all the equilibria associated with every trial value of the structural parameters.

scholarly journals On Bayesian procedure for maximum earthquake magnitude estimation

2012 ◽  
Vol 2 (1) ◽  
pp. 7 ◽  
Author(s):  
Andrzej Kijko
Keyword(s):  
Maximum Likelihood ◽  
Posterior Distribution ◽  
Ad Hoc ◽  
Likelihood Function ◽  
Fundamental Problem ◽  
Likelihood Estimation ◽  
Earthquake Magnitude ◽  
Bayesian Estimator ◽  
Bayesian Procedure ◽  
Posterior Estimate

This work is focused on the Bayesian procedure for the estimation of the regional maximum possible earthquake magnitude <em>m</em><sub>max</sub>. The paper briefly discusses the currently used Bayesian procedure for m<sub>max</sub>, as developed by Cornell, and a statistically justifiable alternative approach is suggested. The fundamental problem in the application of the current Bayesian formalism for <em>m</em><sub>max</sub> estimation is that one of the components of the posterior distribution is the sample likelihood function, for which the range of observations (earthquake magnitudes) depends on the unknown parameter <em>m</em><sub>max</sub>. This dependence violates the property of regularity of the maximum likelihood function. The resulting likelihood function, therefore, reaches its maximum at the maximum observed earthquake magnitude <em>m</em><sup>obs</sup><sub>max</sub> and not at the required maximum <em>possible</em> magnitude <em>m</em><sub>max</sub>. Since the sample likelihood function is a key component of the posterior distribution, the posterior estimate of <em>m^</em><sub>max</sub> is biased. The degree of the bias and its sign depend on the applied Bayesian estimator, the quantity of information provided by the prior distribution, and the sample likelihood function. It has been shown that if the maximum posterior estimate is used, the bias is negative and the resulting underestimation of <em>m</em><sub>max</sub> can be as big as 0.5 units of magnitude. This study explores only the maximum posterior estimate of <em>m</em><sub>max</sub>, which is conceptionally close to the classic maximum likelihood estimation. However, conclusions regarding the shortfall of the current Bayesian procedure are applicable to all Bayesian estimators, <em>e.g.</em> posterior mean and posterior median. A simple, <em>ad hoc</em> solution of this non-regular maximum likelihood problem is also presented.

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 Note on the Existence of the Location Parameter Estimate of the Three-Parameter Weibull Model Using the Weibull Plot

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Chanseok Park
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Weibull Model ◽  
Parameter Estimate ◽  
Reliability Engineering ◽  
Bounded Interval ◽  
Weibull Plot ◽  
Sample Correlation

The Weibull model is one of the widely used distributions in reliability engineering. For the parameter estimation of the Weibull model, there are several existing methods. The method of the maximum likelihood estimation among others is preferred because of its attractive statistical properties. However, for the case of the three-parameter Weibull model, the method of the maximum likelihood estimation has several drawbacks. To avoid the drawbacks, the method using the sample correlation from the Weibull plot is recently suggested. In this paper, we provide the justification for using this new method by showing that the location estimate of the three-parameter Weibull model exists in a bounded interval.

MLML2R: an R package for maximum likelihood estimation of DNA methylation and hydroxymethylation proportions

2019 ◽  
Vol 18 (1) ◽  
Author(s):  
Samara F. Kiihl ◽  
Maria Jose Martinez-Garrido ◽  
Arce Domingo-Relloso ◽  
Jose Bermudez ◽  
Maria Tellez-Plaza
Keyword(s):  
Dna Methylation ◽  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Analytical Form ◽  
R Package ◽  
Maximum Likelihood Estimates ◽  
Computational Time ◽  
Iterative Approximation ◽  
Sequencing Technologies ◽  
Combining Data

Abstract Accurately measuring epigenetic marks such as 5-methylcytosine (5-mC) and 5-hydroxymethylcytosine (5-hmC) at the single-nucleotide level, requires combining data from DNA processing methods including traditional (BS), oxidative (oxBS) or Tet-Assisted (TAB) bisulfite conversion. We introduce the R package MLML2R, which provides maximum likelihood estimates (MLE) of 5-mC and 5-hmC proportions. While all other available R packages provide 5-mC and 5-hmC MLEs only for the oxBS+BS combination, MLML2R also provides MLE for TAB combinations. For combinations of any two of the methods, we derived the pool-adjacent-violators algorithm (PAVA) exact constrained MLE in analytical form. For the three methods combination, we implemented both the iterative method by Qu et al. [Qu, J., M. Zhou, Q. Song, E. E. Hong and A. D. Smith (2013): “Mlml: consistent simultaneous estimates of dna methylation and hydroxymethylation,” Bioinformatics, 29, 2645–2646.], and also a novel non iterative approximation using Lagrange multipliers. The newly proposed non iterative solutions greatly decrease computational time, common bottlenecks when processing high-throughput data. The MLML2R package is flexible as it takes as input both, preprocessed intensities from Infinium Methylation arrays and counts from Next Generation Sequencing technologies. The MLML2R package is freely available at https://CRAN.R-project.org/package=MLML2R.

Maximum likelihood estimation for symmetric α-stable Ornstein–Uhlenbeck processes

2020 ◽  
pp. 2150018
Author(s):  
Zhifen Chen ◽  
Xiaopeng Chen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Transition Function ◽  
Closed Form Expression ◽  
Discrete Observations ◽  
Form Expression ◽  
Probability Density Function Pdf ◽  
Accuracy And Stability

In this paper, we consider the maximum likelihood estimation for the symmetric [Formula: see text]-stable Ornstein–Uhlenbeck (S[Formula: see text]S-OU) processes based on discrete observations. Since the closed-form expression of maximum likelihood function is hard to obtain in the Lévy case, we choose a mixture of Cauchy and Gaussian distribution to approximate the probability density function (PDF) of the S[Formula: see text]S distribution. By means of transition function and Laplace transform, we construct an explicit approximate sequence of likelihood function, which converges to the likelihood function of S[Formula: see text]S distribution. Based on the approximation of likelihood function we give an algorithm for computing maximum likelihood estimation. We also numerically simulate some experiments which demonstrate the accuracy and stability of the proposed estimator.

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